Topology

1. Front Matter

   Pages i-xii

   PDF

2. Introduction

   • Stefan Waldmann

   Pages 1-3

3. Topological Spaces and Continuity

   • Stefan Waldmann

   Pages 5-40

4. Construction of Topological Spaces

   • Stefan Waldmann

   Pages 41-57

5. Convergence in Topological Spaces

   • Stefan Waldmann

   Pages 59-71

6. Compactness

   • Stefan Waldmann

   Pages 73-86

7. Continuous Functions

   • Stefan Waldmann

   Pages 87-110

8. Baire’s Theorem

   • Stefan Waldmann

   Pages 111-124

9. Back Matter

   Pages 125-136

   PDF

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.

• Point Set Topology
• Topological Space and Continuity
• Topology

“Stefan Waldmann’s Topology provides a fast-moving introduction to the core concepts of topology. … this is a well put-together introduction to most of the fundamental topics of topology necessary for the study of advanced mathematics. A student well-versed in the notions of set theory and metric spaces should find this an appropriate introductory resource for topology. Additionally, the book provides a very nice and conveniently compact reference for the standard topics of general topology … .” (Keith Jones, MAA Reviews, June, 2015)

“This nifty little volume brings to a broad English-speaking audience the lectures on topology that Waldmann … gave at Erlangen in the summer of 2012. … Readers should note the decent index, the short but surprisingly far-flung list of references, the many exercises, and the goodly number of illustrative figures, many delicately spot-colored for greater intelligibility, that round out this work. Summing Up: Recommended. Graduate students, researchers/faculty, and professionals.” (F. E. J. Linton, Choice, Vol. 52 (6), February, 2015)

“The book is built as a series of lecture notes on topology, a classical and fundamental part of mathematics which should be known by every student, offering a first introduction to this topic. The text is self-contained and enriched with many exercises which enable the students to consolidate the notions discussed in the core of the course. … The book is a valuable asset for self-study for students and can be recommended as a solid basis of a topology course.” (Corina Mohorianu, zbMATH, Vol. 1301, 2015)

• Julius Maximilian University of Würzburg, Würzburg, Germany

  Stefan Waldmann

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.

Policies and ethics