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Topic: List of general topology topics


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  Learn more about General equilibrium in the online encyclopedia.   (Site not responding. Last check: 2007-11-05)
General equilibrium theory is a branch of theoretical microeconomics.
The modern conception of general equilibrium is provided by a model developed jointly by Kenneth Arrow and Gerard Debreu in the 1950s.
General equilibrium models show what the economy would have to be like for an unregulated economy to be Pareto efficient.
www.onlineencyclopedia.org /g/ge/general_equilibrium.html   (1825 words)

  
  Topology - Wikipedia, the free encyclopedia
Topology has sometimes been called rubber-sheet geometry, because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing).
Internally to the subject, elementary topology is often called point-set topology or general topology, to distinguish it from more advanced areas such as algebraic topology (which grew out of combinatorial topology), geometric topology and low-dimensional topology dealing for example with knot theory, and differential topology.
In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
en.wikipedia.org /wiki/Topology   (1548 words)

  
 PlanetMath: topics on low dimensional topology
List of topic on low dimensional topology that should be here at PM Manifolds in general
"topics on low dimensional topology" is owned by juanman.
This is version 11 of topics on low dimensional topology, born on 2006-06-22, modified 2007-01-06.
planetmath.org /encyclopedia/TopicsOnLowDimensionalTopology.html   (94 words)

  
 Encyclopedia: Topology-glossary   (Site not responding. Last check: 2007-11-05)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
In topology, a subbase (or subbasis) for a topological space X with topology T is a subcollection B of T such that every open set in T can be written as a union of finite intersections of elements of B. We say that the subbase generates the topology T, and...
Algebraic topology is the study of topologically invariant abstract algebra constructions on topological spaces.
www.nationmaster.com /encyclopedia/Topology_glossary   (12332 words)

  
 Topology Summary
Topology is the study of the properties of spaces that are insensitive to continuous deformations.
Topology has sometimes been called rubber-sheet geometry, because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing).
In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
www.bookrags.com /Topology   (6184 words)

  
 General topology - Wikipedia, the free encyclopedia
In mathematics, general topology or point-set topology is the branch of topology which studies elementary properties of topological spaces and structures defined on them.
Set-theoretic topology examines such questions when they have substantial relations to axiomatic set theory, as is often the case.
Other main branches of topology are algebraic topology, geometric topology, and differential topology.
www.wikipedia.org /wiki/General_topology   (235 words)

  
 topology.eu   (Site not responding. Last check: 2007-11-05)
Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry.
The most basic division within topology is into point-set topology, which investigates such concepts as compactness, connectedness, countability, and algebraic topology, which investigates such concepts as homotopy, homology, and knot theory.
General topology, or point-set topology, defines and studies properties of spaces and maps such as connectedness, compactness and continuity.
www.topology.eu   (1686 words)

  
 General topology - Encyclopedia, History, Geography and Biography
It grew out of a number of areas, such as the detailed study of sets of points (as subsets of the real line, understood), the manifold concept, the metric spaces and the early days of functional analysis.
It captures, one might say, almost everything in the intuition of continuity, in a technically adequate form that can be applied in every area of mathematics.
See glossary of general topology for detailed definitions; and the list of general topology topics.
www.arikah.net /encyclopedia/Point_set_topology   (241 words)

  
 EARLY CHILDHOOD ASSOCIATELIST
Topics may include, but are not limited to, sets, logic, probability, statistics, matrices, mathematical systems, geometry, topology, mathematics of finance, and modeling.
Topics include implementation of goals, principles of supervision, budgeting and financial management, and meeting the standards for a NC Child Day Care license.
Topics include the history and selection of developmentally appropriate children’s literature and the use of books and other media to enhance language and literacy in the classroom.
www.sandhills.cc.nc.us /edu/earlychildhoodlist.html   (2029 words)

  
 [No title]   (Site not responding. Last check: 2007-11-05)
In architecture, topology is a term used to describe spatial effects which can not be described by topography, i.e., social, economical, spatial or phenomenological interactions.
In mathematics, topology is a branch concerned with the study of topological spaces.
Johann Benedict Listing (1808-1882) in "Vorstudien zur Topologie," Vandenhoeck und Ruprecht, G├Âttingen, pp.
en-cyclopedia.com /wiki/Topology   (1239 words)

  
 Topology glossary   (Site not responding. Last check: 2007-11-05)
Although there is no clear distinction between different areas of topology, this glossary focuses primarily on general topology and on definitions that are fundamental to a broad range of areas.
A collection of open sets is a subbase (or subbasis) for a topology if every open set in the topology is a union of finite intersections of sets in the subbase.
The weak topology on a set, with respect to a collection of functions from that set into topological spaces, is the coarsest topology on the set which makes all the functions continuous.
www.sciencedaily.com /encyclopedia/topology_glossary   (3722 words)

  
 List of lists of mathematical topics   (Site not responding. Last check: 2007-11-05)
The 20 topics for the IE examination are shown in Figure 2.
List of formal language and literal string topics
List of harmonic analysis and representation theory topics
hallencyclopedia.com /List_of_lists_of_mathematical_topics   (391 words)

  
 directopedia : Directory : Science : Math : Topology
Internally to the subject, elementary topology is often called point-set topology or general topology, to distinguish it from more advanced areas such as algebraic topology (which grew out of combinatorial topology), geometric topology and low-dimensional topology dealing for example with knot theory, and differential topology.
"Topology", its English form, was introduced in print by Solomon Lefschetz in 1930 to replace the earlier name "analysis situs".
General topology, or point-set topology, defines and studies some useful properties of spaces and maps, such as connectedness, compactness and continuity.
www.directopedia.org /directory/Science-Math/Topology.shtml   (2012 words)

  
 Text: Elementary Topology
The purpose of this text is to provide an one semester introduction to topology at an advanced undergraduate, or beginning graduate level.
The most common introduction to topology is through the study of general topology, either beginning with an axiomatic point of view, or perhaps with metric spaces.
Topics of general topology, not relevant to n-space, are not excluded, but are relegated to a coordinated Appendix.
www.math.uiowa.edu /~roseman/et/et.html.old   (719 words)

  
 Matches for:   (Site not responding. Last check: 2007-11-05)
It is remarkable how most of the topics continue to be important today.
Originally published in 1893 and reissued by the AMS in 1911, we are pleased to bring this work into print once more with this new edition.
There are a few other topics covered in the lectures which are somewhat removed from Klein's own work.
www.mathaware.org /bookstore?fn=20&arg1=chelsealist&item=CHEL-339-H   (567 words)

  
 Topology and its Applications   (Site not responding. Last check: 2007-11-05)
Topology and its Applications is a research journal devoted to many areas of topology, and is published by Elsevier Science B.V. in Amsterdam.
It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal.
The journal occasionally publishes "Special Issues." Typically these are centered around a particular topic, research related to the works of an individual, or papers presented at a focused research conference.
www.math.ucsb.edu /~long/TAIA/TopApp.htm   (710 words)

  
 LIST OF ARTICLES BY CATEGORY   (Site not responding. Last check: 2007-11-05)
None of these are yet comprehensive or up-to-date, but filling in or creating these lists will create an easy way to track articles by their categories, as well as creating an implicit to-do list of topics for which articles have not yet been written.
List of astronomical topics, expanded list of topics from N-Z
List of anomalous phenomenon (paranormal) and parapsychology topics
www.websters-online-dictionary.org /definition/LIST+OF+ARTICLES+BY+CATEGORY   (307 words)

  
 Amazon.com: General Topology: Books: Stephen Willard   (Site not responding. Last check: 2007-11-05)
Among the best available reference introductions to general topology, this volume encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by 9 sections on connectivity properties, topological characterization theorems, and homotopy theory.
One of the purest and most intellectually challenging branches of modern mathematics, general topology is not a subject for the faint hearted.
Many of the "standard spaces" of general topology are introduced and examined in the large number of related problems accompanying each section.
www.amazon.com /General-Topology-Stephen-Willard/dp/0486434796   (1337 words)

  
 MATH - Mathematics
Topics (when three credits are completed) include a review of sets, operations with polynomial and rational expressions, solving various types of equations and inequalities and an introduction to coordinate plane and functions.
MATH 514 Topics in Advanced Mathematics for Engineers 3 Basic methods of analysis: introduction to complex variables; special functions including Bessel functions and Legendre polynomials; Fourier series and integrals; partial differential equations; and emphasis on engineering applications.
Possible topics are the theory of queues, dams and inventories, replacement and reliability, probability models in population growth and biomathematics, Monte Carlo simulation, algorithmic methods in probability and operational methods.
www.udel.edu /provost/ugradcat/ugradcat95/26/list/61.html   (3062 words)

  
 Index pages for non-MSC topics
Occasionally however we find topics which are arguably cohesive branches of mathematics, but which have over the last few decades not been accorded an MSC heading of their own.
Topics in Approximations and expansions and Sequences and series are usually also included in calculus courses.
Next we mention some topics often associated with mathematics, but whose primary content is rather free of mathematical ideas -- in particular, these are topics about which a mathematician is unlikely to offer the best surveys.
www.math.niu.edu /~rusin/known-math/index/green.html   (1157 words)

  
 ::: CEE UCL HelpDesk: Listserv :::   (Site not responding. Last check: 2007-11-05)
When you join any mailing list, you will be assigned a default set of list options that control such things as way you received mail when it is distributed and the type of notification LISTSERV will give you when it distributes mail you have sent to a list.
A mailing list to which you are subscribed may support the separation of its mail into a set of topics.
If a list owner has defined a variety of different discussion topics for a list, you may use the TOPICS: option to select those that are of interest to you and exclude all others.
www.cee.odu.edu /uclhd/uclhd_listserv.php   (8018 words)

  
 Topology   (Site not responding. Last check: 2007-11-05)
When the discipline was first introduced it was called analysis situs (Latin analysis of place).
Topology is concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms).
Two figures that can be deformed one into the other are called homeomorphic, and are considered to be the same from the topological point of view.
www.usedaudiparts.com /search.php?title=Topology   (1315 words)

  
 The Math Forum - Math Library - Topology   (Site not responding. Last check: 2007-11-05)
General Topology preprints, from the U.C. Davis front end for the xxx.lanl.gov e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives.
Thus it is a kind of generalized geometry (we are still interested in spheres and cubes, for example, but we might consider them to be "the same", yet distinct from a bicycle tire, which has a "hole") or a kind of generalized analysis...
An list of suggestions for projects in geometry, topology, symmetry, making geometric solids, calendars, spherical and hyperbolic trigonometry, puzzles, models, etc. Projects were to be exhibited at the Geometry Fair at the end of the course.
mathforum.org /library/topics/topology   (2425 words)

  
 User:AndrewKepert - Wikipedia, the free encyclopedia
I included a note about classifying numbers as interesting/uninteresting, as it had crossed my mind to list on the page (or section as it was then) for 38 that its only interesting property was that it was the smallest uninteresting number.
At the time wikipedia had "interesting" properties listed for all numbers 1 to 37 (disclaimer: some of these I wrote).
So this was not an original thought, just a whimsical comment on the process of identifying interesting properties for numbers to put in wikipedia.
www.wikipedia.org /wiki/User:AndrewKepert   (647 words)

  
 Text: Elementary Topology
Topics of general topology, not relevant to n-space, are not excluded, but are relegated to coordinated optional sections.
It is an extensive list of topics, collected as examples, propositions.
Sections marked with asterisk are optional topics from the point of view of general topology.
www.math.uiowa.edu /~roseman/et/et.html   (786 words)

  
 Topology glossary   (Site not responding. Last check: 2007-11-05)
The topology generated by a base is the smallest topology containing the base elements; this topology consists of all unions of elements of the base.
The topology generated by a subbase is the smallest topology containing the subbase elements; this topology consists of all finite intersections of unions of elements of the subbase.
If X is a space and A is a subset of X, then the subspace topology on A induced by X consists of all intersections of open sets in X with A.
www.portaljuice.com /topology_glossary.html   (2482 words)

  
 Graduate Courses
Topics include sequences of numbers, limits and the Cauchy criterion, continuous functions, differentiation, inverse function theorem, Riemann integration, sequences and series, uniform convergence.
Topics will be chosen from a broad range, among the possibilities being reaction kinetic, biological oscillations, population ecology, developmental biology, neurobiology, epidemiology, physiological fluid dynamics, sensory biology, etc. [TOC]
Potential topics include diffusion, stationary solutions, traveling waves, linear stability analysis, scaling and dimensional analysis, perturbation methods, variational and phase space methods, kinematics and laws of motion for continuous media.
www.math.buffalo.edu /gr_course_list.html   (2399 words)

  
 Math > Topology > General Topology at b2bYellowpages.com Subject Directory   (Site not responding. Last check: 2007-11-05)
General Topology Gudunov - Database and tables explaining the logical mesh.
Oxford Analytic Topology Research Group - Research interests: topology of metric spaces, generalised metric spaces, continua, function spaces, hyperspaces, topological algebra, set theoretic methods in topology, and applications of topology to computer science and the theory of differential equations.
Textbook in Problems on Elementary Topology - The core of the book is the material included usually into the Topology part of the two year geometry course in the Mathematical Department of St. Petersburg University.
www.b2byellowpages.com /web.cgi/Science/Math/Topology/General_Topology   (557 words)

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