Czes Kosniowski's A First Course in Algebraic Topology PDF

By Czes Kosniowski

ISBN-10: 0521298644

ISBN-13: 9780521298643

This self-contained creation to algebraic topology is appropriate for a few topology classes. It contains approximately one region 'general topology' (without its ordinary pathologies) and 3 quarters 'algebraic topology' (centred round the primary staff, a comfortably grasped subject which provides a good suggestion of what algebraic topology is). The booklet has emerged from classes given on the collage of Newcastle-upon-Tyne to senior undergraduates and starting postgraduates. it's been written at a degree so as to allow the reader to take advantage of it for self-study in addition to a path booklet. The technique is leisurely and a geometrical flavour is clear all through. the numerous illustrations and over 350 workouts will turn out beneficial as a instructing reduction. This account can be welcomed via complicated scholars of natural arithmetic at schools and universities.

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Extra resources for A First Course in Algebraic Topology

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Prove that X is Hausdorff if and only if Y is Hausdorff. The Hausdorff condition is an example of a separation condition. We shall define some of the other separation conditions, but apart from the next few pages we shall only pursue the Hausdorff condition in detail. 3 Definition Let k be one of the integers 0,1,2,3 or 4. A space X is said to be a 51 Hausdorff spaces Tk-space if it satisfies condition Tk given below: T0: For every pair of distinct points there is an open set containing one of them but not the other.

From previous results we may now deduce that each of the following spaces is compact: (closed bounded subset of (surjective image of Si'); R the Möbius strip (closed bounded subset of R3). 13 Exercises (a) Which of the following spaces are compact? = {xE f (s,t)E < 1 }, f x R2;Os< 1,O

Show that the inclusion map S X is continuous. e. the least number of open sets) such that the inclusion S -+ X is continuous. (d) X is a topological space, S is a subset and i: S X denotes the inclusion map. The set S is given a topology such that for every space Y and map f: Y f: Y S is continuous S if: Y -÷ X is continuous. Prove that the topology on S is the topology induced by the topology on X. (e) Let Y be a subspace of X and let A be a subset of Y. Denote by the closure of A in Y. Clx(A) the closure of A in X and by Prove that Clx(A).

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A First Course in Algebraic Topology by Czes Kosniowski


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