• Elementary Topology: Second Edition by Michael C. Gemignani
  Superb introduction to rapidly expanding area of mathematical thought. Fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory and other essentials. Numerous exercises, plus section on paracompactness and complete regularity. References throughout. Includes 107 illustrations.
  Amazon.com: Elementary Topology: Second Edition (Dover Books on Mathematics) (9780486665221): Michael C. Gemignani: Books
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  in Educational > Mathematics > Topology Books with book books general introduction math mathematical mathematics technology topology
  Note: Recommended by John Banks.
• Introduction to General Topology by Joshi - amazon.com
  K. D. Joshi, Introduction to General Topology. A Halsted Press Book. John Wiley & Sons, Inc., New York, 1983. xii+412 pp. ISBN: 0-470-27556-1. K D Joshi obtained his Ph D in Mathematics from Indiana University,USA in 1972 and has been teaching mathematics at IIT Bombay since 1975. He has been involved with the conduct of the Joint Entrance Examination (JEE) in various capacities for over two decades. He has many books to his credit one of which is Calculus for Scientists and Engineers published by Narosa Publishing House in 2002.
  Amazon.com: Introduction to General Topology (9780852264447): K.D. Joshi: Books
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  in Educational > Mathematics > Topology Books with book books general indian institute introduction joshi mathematical mathematics technology topology
  Note: Really good book. Lots of explaining of motivation, wordy in a good way. His personal homepage is found here: http://www.math.iitb.ac.in/~kdjoshi/ Melbourne Uni Maths library has a copy.
• Topology (2nd Edition) - by James Munkres - amazon.com
  This introduction to topology provides separate, in-depth coverage of both general topology and algebraic topology. Includes many examples and figures. GENERAL TOPOLOGY. Set Theory and Logic. Topological Spaces and Continuous Functions. Connectedness and Compactness. Countability and Separation Axioms. The Tychonoff Theorem. Metrization Theorems and paracompactness. Complete Metric Spaces and Function Spaces. Baire Spaces and Dimension Theory. ALGEBRAIC TOPOLOGY. The Fundamental Group. Separation Theorems. The Seifert-van Kampen Theorem. Classification of Surfaces. Classification of Covering Spaces. Applications to Group Theory. For anyone needing a basic, thorough, introduction to general and algebraic topology and its applications.
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  Note: John Banks recommended it. More formal than gemignani's 'elementary topology'.
• Topology Without Tears, chapters 1-10.
  "Topology Without Tears" by Sidney A. Morris. University of Ballarat, Victoria Australlia.
  in Educational > Mathematics > Topology Books with a analysis mathematics maths morris signey tears textbook topology without
• Beginning Topology (Brooks/Cole Series in Advanced Mathematics) by Sue Goodman
  With a nice balance of mathematical precision and accessibility, this text provides a broad introduction to the field of topology. Author Sue Goodman piques student curiosity and interest without losing necessary rigor so that they can appreciate the beauty and fun of mathematics. The text demonstrates that mathematics is an active and ever-changing field with many problems still unsolved, and students will see how the various areas of mathematics ? algebra, combinatorics, geometry, calculus, and differential equations ? interact with topology. Students learn some of the major ideas and results in the field, do explorations and fairly elementary proofs, and become aware of some recent questions.
  Amazon.com: Beginning Topology (Brooks/Cole Series in Advanced Mathematics) (9780534424268): Sue Goodman: Books
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  Note: A good broad introduction into some topological applications (a good 'overview' of what topology encompasses too); the four-colour problem, fixed-point theorems, fundamental theorem of algebra and knots. Glosses over point-set, seems to cover the important stuff. Her personal website can be found h ...moreere: http://www.math.unc.edu/Faculty/seg/ She recommends a history of Topology here: http://www-gap.dcs.st-and.ac.uk/~history/PrintHT/Topology_in_mathematics.html (I think Brian Davey also recommended this site)
• Elements of general topology by Donald Bushaw (2nd edition)
  Author: Bushaw, Donald. Title: Elements of general topology. Published: New York : J. Wiley, [1963].
  in Educational > Mathematics > Topology Books with book bushaw donald education educational math mathematics topology
  Note: A really good, well worded account on point set topology, gives a good sketch of the motivation behind definitions. LTU Bundy's got it: https://alpha2.latrobe.edu.au/patroninfo/1119178/item&1287918
• Proof: "any topological space with the fixed point property is connected" - PlanetMath
  Theorem Any topological space with the fixed-point property is connected. Proof. We will prove the contrapositive. ....
  in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups with concept fixed fundamental math mathematical mathematics planetmath point proof property topology
  Note: A decent explanation of the fixed point property: http://planetmath.org/encyclopedia/FixedPointProperty.html
• Algebraic Topology by Allen Hatcher
  A bunch of books written by Allen Hatcher, in particular Algebraic Topology (described below) recommended by Grant... This is the first in a series of three textbooks in algebraic topology having the goal of covering all the basics while remaining readable by newcomers seeing the subject for the first time. The first book contains the basic core material along with a number of optional topics of a relatively elementary nature. The other two books, which are largely independent of each other, are provisionally titled "Vector Bundles and K-Theory" and "Spectral Sequences in Algebraic Topology."
  A downloadable textbook in algebraic topology
  algebraic topology
  in Educational > Mathematics > Topology Books with algebraic basics book books education educational elementary newcomers textbooks topology
  Note: $30 off Amazon.com: http://www.amazon.com/Algebraic-Topology-Allen-Hatcher/dp/0521795400/ref=pd_bbs_sr_1/102-7670573-1396111?ie=UTF8&s=books&qid=1179353668&sr=8-1
• Fixed point property - Wikipedia
  In mathematics, a topological space X has the fixed point property if all continuous mappings from X to X have a fixed point.
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  in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups with community-based community-driven educational fixed math mathematics maths point property theorem topology uni university wiki wikipedia wikipedia.org
  Note: In mathematics, a fixed point (sometimes shortened to fixpoint) of a function is a point that is mapped to itself by the function... http://en.wikipedia.org/wiki/Fixed_point_%28mathematics%29
• Fixed Point Theorem Finite-Closed - Topology Q+A Board
  Does a space which has the finite closed topology have the fixed-point property? I really don't know how to go about this, but my initial thoughts are: - This should be related to continuous functions and connectedness.
  in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups with closed finite fixed help mathematical maths point theorem topology tops
• Fixed-point theorem - Wikipedia
  In mathematics, a fixed-point theorem is a result saying that a function F will have at least one fixed point (a point x for which F(x) = x), under some conditions on F that can be stated in general terms. Results of this kind are amongst the most generally useful in mathematics. The Banach fixed point theorem gives a general criterion guaranteeing that, if it is satisfied, the procedure of iterating a function yields a fixed point. By contrast, the Brouwer fixed point theorem is a non-constructive result: it says that any continuous function from the closed unit ball in n-dimensional Euclidean space to itself must have a fixed point, but it doesn't describe how to find the fixed point (See also Sperner's lemma).
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  in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups with community-based community-driven educational fixed math mathematics maths point property theorem topology uni university wiki wikipedia wikipedia.org
• Open problems in topology edited by Jan van Mill, George M. Reed.
  Title: Open problems in topology / edited by Jan van Mill, George M. Reed. Published: Amsterdam [Netherlands] ; New York : North-Holland ; New York, N.Y., U.S.A : Distributors for the U.S. and Canada, Elsevier Science Pub. Co., 1990.
  in Educational > Mathematics > Topology Books with education educational graduate honours math mathematical mathematics open thesis topology
  Note: Doesn't seem like they got to their third edition, despite saying it was due around 1995. Need to know a lot more topology before I can understand the problems.
• Separation axiom - Wikipedia
  In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are axioms only in the sense that, when defining the notion of topological space, you could add these conditions as extra axioms to get a more restricted notion of what a topological space is. The modern approach is to fix once and for all the axiomatization of topological space and then speak of kinds of topological spaces.
  in Educational > Mathematics > Ideas/Explanations/Wiki or Mathworld lookups with axiom axioms concept fundamental math mathematical mathematics separation topology wiki wikipedia
  Note: See also: The precise meanings of the terms associated with the separation axioms has varied over time, as explained in History of the separation axioms... http://en.wikipedia.org/wiki/History_of_the_separation_axioms

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