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Topic: General topology

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	Topology - Wikipedia, the free encyclopedia
		Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces.
		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).
		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 (1352 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.
	en.wikipedia.org /wiki/General_topology (235 words)

	54: General topology
		Topology is the study of sets on which one has a notion of "closeness" -- enough to decide which functions defined on it are continuous.
		Thus a general theme in topology is to test the extent to which the axioms force the kind of structure one expects to use and then, as appropriate, introduce other axioms so as to better match the intended application.
		Generalizations of Kuratowski embedding theorem to higher-dimensional complexes: citations to literature.
	www.math.niu.edu /~rusin/known-math/index/54-XX.html (2431 words)

	Topology Seminar (Site not responding. Last check: 2007-11-07)
		In general, the exponentiable spaces are known to be precisely the core-compact spaces.
		Given the generality of the question, the answer is surprisingly elegant, and you don't really need to know anything more than the meaning of compact and Hausdorff to follow the talk.
		Point-free topology is a part of this area, and consist of the study of certain lattices called frames.
	www.cs.bham.ac.uk /research/events/topology-seminar/topology.html (2602 words)

	55: Algebraic topology
		Algebraic topology is the study of algebraic objects attached to topological spaces; the algebraic invariants reflect some of the topological structure of the spaces.
		General topology focuses on the underlying spaces and is often concerned with fairly analytical issues (e.g.
		The tools of algebraic topology, when developed in isolation or for applications to other fields such as ring theory, give rise to homological algebra and category theory; this is the proper framework for comparing different algebraic tools.
	www.math.niu.edu /~rusin/known-math/index/55-XX.html (2581 words)

	General Topology Science, Directory (Site not responding. Last check: 2007-11-07)
		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.
		Topology Atlas A multi-purpose center for electronic distribution of information related to topology.
		Textbook-Ã¡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.wacofdn.org /d2RjXzI2OTQ1.aspx (169 words)

	The Math Forum - Math Library - Topology (Site not responding. Last check: 2007-11-07)
		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.
		A short article designed to provide an introduction to general topology, the study of sets on which one has a notion of "closeness" - enough to decide which functions defined on it are continuous.
		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...
	mathforum.org /library/topics/topology (2459 words)

	ODP: Science:Math:Topology:General Topology (Site not responding. Last check: 2007-11-07)
		Topology Atlas - A multi-purpose center for electronic distribution of information related to topology.
		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.
	beta.thesoftwarestudio.com /Science,Math,Topology,General_Topology.html (243 words)

	Topology - Wikibooks
		General Topology is based solely on set theory and concerns itself with structures of sets.
		It is at its core a generalization of the concept of distance, though this will not be immediately apparent for the novice student.
		Topology generalises many distance related concepts, such as continuity, compactness and convergence.
	en.wikibooks.org /wiki/Topology (252 words)

	General topology (Site not responding. Last check: 2007-11-07)
		In mathematics, general topology or point settopology is that branch of topology which studies elementary properties of topological spaces and structures defined on them.
		It captures, one might say, almosteverything in the intuition of continuity, in a technically adequate form thatcan be applied in every area of mathematics.
		Other main branches of topology are algebraic topology, geometrictopology, and differential topology.
	www.therfcc.org /general-topology-35860.html (195 words)

	Basic Library List-Topology
		General Topology I: Basic Concepts and Constructions, Dimension Theory New York, NY: Springer-Verlag, 1990.
		Elements of Mathematics: General Topology New York, NY: Springer-Verlag, 1989.
		From Geometry to Topology Philadelphia, PA: Crane, Russak, 1974.
	www.maa.org /BLL/topology.htm (866 words)

	Stone-Cech Compactification - NoiseFactory Science Archives (http://noisefactory.co.uk)
		[See also: Introduction to General Topology] General topology is that branch of pure mathematics that concerns itself with the nature of continuity.
		In general, however, we usually just talk about X and assume that the topology can be taken for granted.
		Topologies can be very general indeed, so we need to impose some restrictions if we're to be able to derive useful results.
	noisefactory.co.uk /maths/stone-cech.html (1649 words)

	Open Directory - Science: Math: Topology (Site not responding. Last check: 2007-11-07)
		Algebraic Topology Discussion List - The primary functions of this list are: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology.
		Topology of Manifolds: Supersymmetry and QFT - This is the web resource page for a course taught by John Morgan in Fall 1997 at Columbia University.
		TTT on WWW - The Transpennine Topology Triangle is a topology seminar partially supported by the London Mathematical Society with vertices at Leicester, Manchester and Sheffield.
	dmoz.org /Science/Math/Topology (299 words)

	Algebraic General Topology and Math Synthesis - Replacement of Mathematical Analysis
		Algebraic General Topology is about how to act with abstract topological objects expressing infinities with algebraic operations.
		This new research field is both just generalizing former analysis and new theorems/concepts not having analogs in old theories.
		Note that Algebraic General Topology being a generalization of General Topology has nothing in common (except of the name) with Algebraic Topology.
	www.mathematics21.org /algebraic-general-topology.html (394 words)

	General Topology - NoiseFactory Science Archives (http://noisefactory.co.uk)
		In general, topological arguments require there to be 'sufficient' open sets, or else 'sufficient' functions, for us to distinguish between points of the underlying set.
		If we assign P the discrete topology, in which every subset is open, these will include all the inverse images of open sets in the various factor spaces.
		The standard topologies on N, Z, Q, and R are all (defined to be) their order topologies.
	noisefactory.co.uk /maths/topology.html (4788 words)

	SSPM Contents (Site not responding. Last check: 2007-11-07)
		This is an introduction to algebraic, geometric and general topology.
		It emerged from several former editions and is today the most complete source and reference book for General Topology.
		It is indispensable in every mathematical library and completes the encyclopedical work of the author in topology.
	www.heldermann.de /SSPM/sspmcont.htm (538 words)

	Open Directory - Science: Math: Topology: General Topology (Site not responding. Last check: 2007-11-07)
		Algebraic General Topology and Math Synthesis - Introduction to Algebraic General Topology and Math Synthesis.
		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.
		Topology - Descriptions and illustrations of several Topological and Differential Geometry related notions.
	www.dmoz.org /Science/Math/Topology/General_Topology (420 words)

	54: General topology (Site not responding. Last check: 2007-11-07)
		The distinction between this and the previous paragraph is that additional axioms are assumed about a new construct provided at the outset, rather than additional axioms about the topology; thus the questions asked about these structures can be about either the topology or about the new construct.
		One significant family of examples is sets S of functions between topological spaces X and Y. Depending on the properties or additional structures possessed by X and Y, S may be given one or more topologies, and in some cases itself possesses an additional structure.
		See 55: Algebraic Topology for the definitions, and computations, and applications of fundamental groups, homotopy groups, homology and cohomology.
	www.math.niu.edu /%7Erusin/papers/known-math/index/54-XX.html (2431 words)

	What is Topology? (Site not responding. Last check: 2007-11-07)
		Basically, topology is the modern version of geometry, the study of all different sorts of spaces.
		Topology is almost the most basic form of geometry there is. It is used in nearly all branches of mathematics in one form or another.
		We use topology to describe homotopy, but in homotopy theory we allow so many different transformations that the result is more like algebra than like topology.
	www.math.wayne.edu /~rrb/topology.html (567 words)

	Bounded weak star and general strict topology (Site not responding. Last check: 2007-11-07)
		Suppose that B is a Banach algebra with bounded approximate identity, and that X is a is a left Banach module over B. The strict topology on X is the topology generated by the set {p_b: b in B} of semi-norms, where p_b(x) = bx
		A final result shows that, if G is a locally compact abelian group with Haar measure, then G is compact if and only if the bounded weak star topology induced in L p(G) (1 < p <=infinity) by Lq(G) (1/q +1/p = 1) is the strict topology induced by L^1(G).
		From this it follows that, in its strict topology, the Banach space of bounded analytic functions on the unit disc is a topological algebra under convolution.
	www.mth.msu.edu /~shapiro/Pubvit/Downloads/BWT_GST/BWST_GST.html (190 words)

	Conference History
		The Summer Conference on Topology and its Applications is an annual event bringing together an international audience of researchers in general topology and related fields.
		The early history of the conference is described in the Preface of General Topology and Applications, (Susan Andima, Ralph Kopperman, Prabudh Misra, Jack Reichman and Aaron Todd, editors.
		In addition to papers in general topology and set theoretic topology, we find here papers with motivations from topological groups and semigroups,convergence structures, functional analysis, topological algebra, category theory, Lie group theory, topological dynamics, computer science and other disciplines.
	sumtopo.home.att.net /history.html (1981 words)

	Amazon.com: Books: Topology (2nd Edition) (Site not responding. Last check: 2007-11-07)
		It covers all the standard material for a first course in general topology starting with a full chapter on set theory, and now in the second edition includes a rather extensive treatment of the elemantary algebraic topology.
		Eventhough a few contending general topology texts --such as a recent title published in the Walter Rudin Series-- have started to hit the academic markets, Munkres will no doubt remain as the classic, tried-&-trusted source of learning and reference for generations of mathematics students.
		Highlights were taken from the first section (point set topology), and a large focus of the class was on the algebraic topology in the second section of the book.
	www.amazon.com /exec/obidos/tg/detail/-/0131816292?v=glance (1878 words)

	Math 671 -- intro to general topology (Site not responding. Last check: 2007-11-07)
		Course goals: The language of basic topology, commonly called "point-set topology", is important to many fields of mathematics, including differential geometry, algebraic topology, and many areas of analysis.
		We will learn all the basic definitions that allow you to say interesting things in the language, together with lots of examples to help develop intuition about what the defintions really mean.
		Although some examples in topology are "exotic", and are mainly useful to remind you that your intution doesn't tell you the whole story, we will spend more time on examples that have real mathematical content.
	www.math.umass.edu /~braden/courses/671F02/671.html (209 words)

	General Topology
		Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students.
		Its treatment 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 nine sections on connectivity properties, topological characterization theorems, and homotopy theory.
		Fresh approach explains nontrivial applications of metric space topology to analysis; topics from elementary algebraic topology focus on concrete results with minimal formalism.
	store.doverpublications.com /0486434796.html (194 words)

	Problems of research interest (from topology) -- Encyclopædia Britannica (Site not responding. Last check: 2007-11-07)
		Many of the problems of research interest in topology are concerned with manifolds and involve an interplay between the methods of general topology and those of algebraic topology (see topology, algebraic).
		More results on "Problems of research interest (from topology)" when you join.
		Provides information on algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g.
	www.britannica.com /eb/article-69129 (850 words)

	Topology Atlas Education: Lecture Notes and Resources (Site not responding. Last check: 2007-11-07)
		Topology Explained is a new and growing collection of notes for people learning topology.
		Topology Course Lecture Notes by Aisling McCluskey (University College Galway, Ireland) and Brian McMaster (The Queen's University of Belfast, Northern Ireland)
		Please use the Topology Q+A Board to ask for help with these resources, or on any other subjects in topology and related areas that you are studying.
	at.yorku.ca /topology/educ.htm (118 words)

	What is topology?
		We can analyse the structure of Y using the methods of algebraic topology, and learn a number of interesting and nontrivial things about it.
		However, if we want to achieve a specified position and orientation of the hand, there will in general be many ways to do this.
		In other words, many different points of X will be associated to the same point of Y. It would be convenient in the design and use of such robots to have a so-called ``inverse mapping''.
	www.shef.ac.uk /~pm1nps/Wurble.html (1402 words)

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