By Czes Kosniowski

This self-contained creation to algebraic topology is acceptable for a couple of topology classes. It includes approximately one zone 'general topology' (without its ordinary pathologies) and 3 quarters 'algebraic topology' (centred round the basic staff, a with no trouble grasped subject which provides a good suggestion of what algebraic topology is). The ebook has emerged from classes given on the college of Newcastle-upon-Tyne to senior undergraduates and starting postgraduates. it's been written at a degree with a view to permit the reader to exploit it for self-study in addition to a path ebook. The strategy is leisurely and a geometrical flavour is obvious all through. the various illustrations and over 350 routines will end up priceless as a instructing reduction. This account might be welcomed via complicated scholars of natural arithmetic at schools and universities.

**Read Online or Download A First Course in Algebraic Topology PDF**

**Similar topology books**

**Real variables with basic metric space topology**

Designed for a primary direction in actual variables, this article encourages intuitive pondering and gives historical past for extra complex mathematical paintings. issues contain advanced variables, degree conception, differential equations, useful research, and chance. precise options to the issues look behind the booklet, making it excellent for self sustaining research.

**Initiation to combinatorial topology**

An basic textual content that may be understood through somebody with a historical past in highschool geometry, Invitation to Combinatorial Topology bargains a stimulating initiation to special topological principles. This translation from the unique French does complete justice to the text's coherent presentation in addition to to its wealthy historic content material.

**Generalized Solutions of Operator Equations and Extreme Elements **

Summary types for lots of difficulties in technology and engineering take the shape of an operator equation. The answer of those difficulties usually calls for opting for the life and distinctiveness of suggestions to those equations. "Generalized options of Operator Equations and severe components" provides lately bought leads to the examine of the generalized suggestions of operator equations and severe components in linear topological areas.

**Introduction to the Qualitative Theory of Dynamical Systems on Surfaces**

This e-book is an creation to the qualitative thought of dynamical platforms on manifolds of low size (on the circle and on surfaces). besides classical effects, it displays the main major achievements during this region got lately via Russian and overseas mathematicians whose paintings has no longer but seemed within the monographic literature.

- Topology of 3-Manifolds and Related Topics
- Elementary Applied Topology
- Simplicial and operad methods in algebraic topology
- Simplicial Homotopy Theory

**Additional info for A First Course in Algebraic Topology**

**Example text**

As a second example first consider the space C { (x,y,z)ER3;x2 +y2 l,IzI< l} with the induced topology. e. M= {{p,-p);pEC}. Since we have a natural surjective map from C to M we can give M the quotient topology; the result is called a Mobius strip or band (sometimes Mobius is spelt Moebius). 28 A first course in algebraic topology Consider the function f: M { R3 given by p,- p } -+ ((x2 - y2) (2+xz), 2xy(2+xz),yz) where p = (x,y,z) E C ç R3. It is not difficult to check that f is injective. 1. 2 below).

B) Prove that the space Y is Hausdorif if and only if the diagonal D = { Y;y1= y2 } in YX Y is a closed subset of YX Y. (c) Let f: X Y be a continuous map. Prove that if Y is Hausdorif then the set { (x1,x2) E X X X; f(x1) = f(x2) } is a closed subset of XXX. (d) Let f: X -+ Y be a map which is continuous, open and onto. Prove that Y is a Hausdorff space if and only if the set (x1,x2) E X X X; f(x1) = f(x2) } is a closed subset of XX X. Let X be a compact Hausdorff space and let Y be a quotient space determined by a map f: X Y.

Proof Suppose that X and Y are compact. Let { W3;j Ci I be an open cover is of the form U (U3 k X VJk) where Uj,k is of X X Y. By definition each kEK X VJ,k;J Ci, kEK} is an open in Xand Vj,k is open in Y. Thus { open cover of X X Y. ,n(x) } x } X Y. ,n(xj) } . is a finite open cover of X X Y. (xj) ç Ui,k X Vj,k c E J ) which covers X X Y. It follows that there is a finite subcover of Conversely if X X Y is compact then X and Y are compact because lrX and iTy are continuous. More generally, of course, if X1 are compact topological spaces is also compact.