
	Where results make sense

Topic: Counterexamples in Topology

Related Topics

Connectedness

In the News (Wed 15 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Basic Library List-Topology
		Counterexamples in Topology, New York, NY: Springer-Verlag, 1978.
		From Geometry to Topology Philadelphia, PA: Crane, Russak, 1974.
		Moise, Edwin E. Geometric Topology in Dimensions 2 and 3 New York, NY: Springer-Verlag, 1977.
	www.maa.org /BLL/topology.htm (866 words)

	Topology - Wikipedia, the free encyclopedia
		Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants.
		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.
	en.wikipedia.org /wiki/Topology (1755 words)

	Counterexample - Wikipedia, the free encyclopedia
		In logic, and especially in its applications to mathematics and philosophy, a counterexample is an exception to a proposed general rule, i.e., a specific instance of the falsity of a universal quantification (a "for all" statement).
		In mathematics, counterexamples are often used to probe the boundaries of possible theorems.
		A mathematical counterexample would be something like this: If you had a theorem that said "all numbers that are not negative are positive," and someone pointed out that zero is not negative, but is also not positive, then zero would be a counterexample.
	en.wikipedia.org /wiki/Counterexample (1085 words)

	Counterexample (Site not responding. Last check: 2007-10-20)
		In mathematics, counterexamples are often used to probe the boundaries of possible theorem s.
		In philosophy, counterexamples are usually used to argue that a certain philosophical position is wrong by showing that it doesn't apply in certain cases.
		But Socrates replies that, because of their strength of numbers, the class of common rabble is stronger than the propertied class of nobles, even though the masses are prima facie of worse character.
	www.serebella.com /encyclopedia/article-Counterexample.html (955 words)

	Counterexamples in Topology - Wikipedia, the free encyclopedia
		Counterexamples in Topology (1978) is a mathematics book by topologists Lynn A. Steen and J.
		Together with their graduate students, Steen and Seebach canvassed the field of topology for a wide grouping of topological counterexamples.
		The answer is yes, as counterexample #3 (the discrete topology on an uncountable set) is the first to show.
	en.wikipedia.org /wiki/Counterexamples_in_Topology (287 words)

	Encyclopedia :: encyclopedia : Trivial topology (Site not responding. Last check: 2007-10-20)
		In topology, a topological space with the trivial topology is one where the only open sets are the empty set and the entire space.
		The trivial topology is the topology with the least possible number of open sets, since the definition of a topology requires these two sets to be open.
		The trivial topology belongs to a pseudometric space in which the distance between any two points is zero, and to a uniform space in which the whole cartesian product X × X is the only entourage.
	www.hallencyclopedia.com /Trivial_topology (533 words)

	Counterexamples in Clifford algebras
		After a counterexample has been presented, it is often easier to settle whether it fulfils all the assumptions than to check all the details of the proof.
		After verification of the validity of a counterexample, further study in the same line, to rescue the "theorem", at whatever generality, is useless and erroneous activity.
		Lounesto: Counterexamples in Clifford algebras with CLICAL, pp.
	www.hut.fi /%7Eppuska/mirror/Lounesto/counterexamples.htm (3687 words)

	Counterexample (Site not responding. Last check: 2007-10-20)
		In logic and especially in its applications to mathematics and philosophy a counterexample is an exception to a proposed rule i.e.
		Counterexamples can exist in Brazilian logic but the argument must be checked to ensure that contradiction produced actually is false in the case at hand.
		But Socrates replies that because of their strength numbers the class of common rabble is than the propertied class of nobles even the masses are prima facie of worse character.
	www.freeglossary.com /Counterexample (948 words)

	Counterexample (Site not responding. Last check: 2007-10-20)
		In mathematics, counterexamples are often used to probe the boundaries ofpossible theorems.
		In philosophy, counterexamples are usually used to argue that a certainphilosophical position is wrong by showing that it doesn't apply in certain cases.
		Callicles might challenge Socrates' counterexample, arguing perhaps that the common rabble really are better than thenobles, or that even in their large numbers, they still are not stronger.
	www.therfcc.org /counterexample-5618.html (856 words)

	Cantor set - Wikipedia, the free encyclopedia
		A closed set in which every point is an accumulation point is also called a perfect set in topology, while a closed subset of the interval with no interior points is nowhere dense in the interval.
		In the relative topology on the Cantor set, the points have been separated by a clopen set.
		The basis for the open sets of the product topology are the cylinder sets; the homeomorphism maps these to the subspace topology that the Cantor set inherits from the natural topology on the real number line.
	en.wikipedia.org /wiki/Cantor_set (1782 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.
		Since the axioms of topology are stated in terms of subsets of X, it should be no surprise that one branch of topology is closely related to set theory, particularly "descriptive set theory".
	www.math.niu.edu /~rusin/known-math/index/54-XX.html (2431 words)

	Topology - Wikibooks, collection of open-content textbooks
		General Topology is based solely on set theory and concerns itself with structures of sets.
		Topology is a generalization of analysis and geometry.
		A naive description of topology is that it identifies those quialities of a space that do not change under twisting and stretching of that space.
	en.wikibooks.org /wiki/Topology (395 words)

	Counterexamples in Topology - Buy Counterexamples in Topology - Read Reviews of Counterexamples in Topology (Site not responding. Last check: 2007-10-20)
		indispensable to those who have occasion to use point-set topology." I don't think this book is intended to be a text (and I think the authors say so), in which case it would be terrible because it doesn't explain the concepts very much.
		A distinct characteristic of point set topology is that it builds on counterexamples.
		The point of point set topology (pun unintended) is too determine what A,B,C are, and to weaken the hypothesis.
	www.allbooks.info /sys/products/item_id:048668735X/search_type:AsinSearch/locale:us (292 words)

	Topology: A First Course Book at Shop Ireland
		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.
		Although not a hot research topic (compared to the rest of topology), it is foundational and as such many have assumed that point set topology could only be presented as a dull prerequisite for more interesting mathematics.
		This book does not really discuss algebraic or geometric topology (besides a discussion of the fundamental group and covering spaces), which for most people are the really interesting parts of topology.
	www.shopireland.ie /books/reviews/0139254951 (1001 words)

	Counterexamples in Analysis (Dover Books on Mathematics) (Site not responding. Last check: 2007-10-20)
		Conversely, every counterexample for the proposition "every perfect number is even" is a perfect number that is not even.
		One well-reviewed book on counterexamples in analysis says that in order to demonstrate that a universal proposition is false it is necessary and sufficient to construct a counterexample.
		Moreover the mere construction of an object that happens to be a counterexample does not by itself demonstrate that it is a counterexample - sufficiency fails.
	www.programming-reviews.com /Counterexamples_in_Analysis_Dover_Books_on_Mathematics_0486428753.html (615 words)

	Counterexamples in Topology - TheBestLinks.com - Cantor set, Euclidean space, Finite, Hilbert space, ... (Site not responding. Last check: 2007-10-20)
		Counterexamples in Topology, Cantor set, Euclidean space, Finite, Hilbert space...
		Counterexamples in Topology is a book by topologists Lynn A. Steen and J.
		who, together with their graduate students, canvassed the field of topology for a wide grouping of topological counterexamples.
	www.thebestlinks.com /Counterexamples_in_Topology.html (195 words)

	Lynn Arthur Steen
		During my first years at St. Olaf I sought and received NSF support for a program of undergraduate research--at that time a rarity in mathematics--to provide a base for St. Olaf graduates to enter strong graduate schools in the mathematical sciences.
		Since my teaching at that time focused on analysis and topology, it was natural to select research topics that grew out of those interests.
		Counterexamples in Topology,co-authored with St. Olaf colleague J. Arthur Seebach, Jr.
	www.stolaf.edu /people/steen/Professional/mathwrit.html (565 words)

	MSc abstract (Site not responding. Last check: 2007-10-20)
		The book Counterexamples in Topology is a useful catalogue of topological spaces and properties.
		The Alexandrov, Scott and weak topologies are described and shown to be examples of this notion.
		The sobriety and sober reflections of specialization topologies are considered, and these motivate a suggestion for a generalization of the notion of a topological space.
	www.maths.ox.ac.uk /~kirby/anlacit_abstract.html (175 words)

	Amazon.de: Counterexamples in Topology: Bücher: Lynn Arthur Steen,J. Arthur Seebach (Site not responding. Last check: 2007-10-20)
		This is an excellent book to really start understanding all the general topology learned in an introductory (undergrad or grad level) class.
		The topologies given vary considerably in level of difficulty.
		Counterexamples in Topology is both useful and enjoyable, particularly for people who benefit from charts and outlines.
	www.amazon.de /exec/obidos/ASIN/048668735X (670 words)

	Alibris: topology
		Useful both as a text for students and as a source of reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory which is most useful for its application in modern analysis.
		Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students.
		Elegant, intuitive approach to topology from self-theoretic topology to Betti groups; how concepts of topology are useful in math and physics.
	www.alibris.com /search/books/subject/topology (1012 words)

	Counterexamples in Topology - www.testbericht-archiv.de (Site not responding. Last check: 2007-10-20)
		It gives you an idea of the areas of topology in a way that is very good and very understandable.
		In short no student of topology should be without this book.
		In the second part, the book provides "Counterexamples": quite a few topologies, both the predictable and the quirky kinds.
	www.testbericht-archiv.de /048668735X/Counterexamples-in-Topology-Test.html (314 words)

	PlanetMath: bibliography for topology
		Counterexamples in Topology, Holt, Rinehart and Winston, Inc., 1970; Springer, New York, 1978; Dover, New York, 1995; ISBN 0-486-68735-X; QA611.3.S74
		Topology in Relation to Other Areas of Mathematics
		This is version 5 of bibliography for topology, born on 2004-09-30, modified 2006-08-14.
	planetmath.org /encyclopedia/BibliographyForTopology.html (169 words)

	Counterexamples in Topology \| Best price for Book
		A distinct characteristic of point set topology is that it thrives on counterexamples.
		In fact, if you thumb through any point set topology text, almost all the theorems are in the form "If the space X is A,B,C, then the space is X,Y,Z".
		A collection of counterexamples presented in this book (excellent organisationm, by the way) is an essential supplement of a topology course, and it might make people 'see' through the whole thing.
	www.shop0nline.com /048668735x.htm (516 words)

	PlanetMath: separation axioms
		Bibliography: Counterexamples in Topology, L. Steen, J. Seebach Jr., Dover Publications Inc. (New York)
		Cross-references: counterexamples, strictly, implications, completely regular space, Hausdorff space, Fréchet space, satisfies, Urysohn function, closed set, closures, disjoint, contain, neighborhood, points, pathological, open sets, separated, topological space
		In topology there seem to be two conventions for the
	www.planetmath.org /encyclopedia/Regular.html (508 words)

	[No title]
		Counterexamples in Topology, Dover, 1995, by L.A. Steen and J.A. Seebach,
		My goal is that by the end of the course you have a clear understanding of the basic topological concepts, are able to use them for proving things, and appreciate importance of topology for other areas of mathematics.
		No one can learn topology merely by pouring over the definitions, theorems and examples that are worked out in the text.
	www-math.cudenver.edu /~puhalski/teaching/99-top/s (252 words)

	Counterexamples in Topology
		A distinct characteristic of point set topology is that it builds on counterexamples.
		A collection of counterexamples presented in this book (excellent organisation, by the way) is an essential supplement of a topology course; it enables one to see between the points, so to speak.
		This is not a book meant to be studied without a regular textbook on topology, only to be used as an overall review of problems and short basic premises of topology.
	www.wbthub.com /Counterexamples-in-Topology-048668735X (419 words)

	The Route To Active Lifestyle - Algebraic Topology
		For the die-hard mathematician who enjoys less fluff, this book is not for you and, in particular, if this is your first venture in Algebriac Topology, you enjoy the theorem-proof-theorem style with a light sprinkling of explaination, then I would recommend J.J. Rotman's text.
		It serves as an introductory text for a graduate level algebraic topology course.
		It is not, however, always suited to be the sole text for a class if the object is to enable students to obtain the tools of algebraic topology and be able to perform proofs and calculations with appropriate mathematical rigor.
	www.activeroute.com /index.php/trade/productinfo/ASIN/0521795400 (742 words)

	Topology Books
		Counterexamples in Topology, Lynn Arthur Steen, J. Arthur Seebach...
		is divided into two parts: an introduction to topology, using metric spaces to motivate the definition of a...
		Introduction to Topology, Theodore W Gamelin, Robert Everist Greene, Dover Publications...
	www.placedirectory.com /books/Topology-books.html (371 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Math 571, Topology, Fall 1998 office hours:Wednesday 10 - 12 or after my classes at the classrooms.
		Steen and Seebach "Counterexamples in Topology" GRADING POLICY: Students are encouraged to look up solutions or to discuss the problem with their friends if they wish.
		I only require that the solution be written in the student's own words, and that any substantial help be cited.
	www.math.purdue.edu /~gottlieb/Courses/math571F98 (104 words)

	» Counterexamples in Topology
		A collection of counterexamples presented in this book (excellent organisation, by the way) is an essential supplement of a topology course; it enables one to 'see' between the points, so to speak.
		This is not a book meant to be studied without a regular textbook on topology, only to be used as an overall review of problems and short basic premises of topology.
		It then shows a basic overview of topology that helps greatly to understand the different fields of topology.
	www.mathreading.com /Shop/Counterexamples-in-Topology/048668735X (776 words)

Try your search on: Qwika (all wikis)