Topology: An Introduction

Front Cover
Springer, Aug 5, 2014 - Mathematics - 136 pages

This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs.

While there are already many excellent monographs on general topology, most of them are too large for a first bachelor course. Topology fills this gap and can be either used for self-study or as the basis of a topology course.

 

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Contents

1 Introduction
2
2 Topological Spaces and Continuity
5
3 Construction of Topological Spaces
41
4 Convergence in Topological Spaces
59
5 Compactness
73
6 Continuous Functions
87
7 Baires Theorem
111
Appendix ANot an Introduction to Set Theory
125
References
131
Index
133
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About the author (2014)

Stefan Waldmann is a mathematician working in mathematical physics. His main interests are in symplectic geometry, Poisson geometry and deformation quantization using methods from locally convex analysis, differential geometry and algebra.

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