topology undergraduate texts in mathematics


What is topology in math?

Roughly speaking, topology is the area of mathematics that studies the “shape” of spaces. More precisely: De?nition 1. A topology on a set X is a collection T of subsets of X such that: (a) the empty set and X are in T ; (b) the union of any subcollection of T is in T ; (c) the intersection of ?nitely many elements of T is in T .

What are some good graduate level point set topology books?

The books by Dugundji and Kelley in the bibliography are excellent graduate level point set topology texts, and each of these views the subject somewhat di erently from the perspective in Munkres and these notes. The following more recent text is also a very good alternate reference for much of the material in this course: T. Lawson.

Should point set topology cover both metric spaces and topological spaces?

Eventually a course in point set topology needs to cover both types of structures, but there is no universal agreement on which should come frst and when the other should be introduced. The approach in these notes will be to introduce metric spaces frst and topological spaces immediately afterwards.

What is a good reference for algebraic topology?

Another excellent reference is Section 5 in Appendix A to Massey, Algebraic Topology: An Introduction (CAUTION: There is a somewhat di erent book by the same author with the very similar title, A Basic Course in Algebraic Topology). 101

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