Topology for the Working Mathematician by Michael Müger
Topology for the Working Mathematician - Table of Contents
PART I: FUNDAMENTALS
- 1. Introduction
- 2. Basic Notions of Point-Set Topology
- 3. Metric Spaces: Completeness and Applications
- 4. More Basic Topology
- 5. Convergence and Continuity
- 6. New Spaces from Old
PART II: COVERING AND SEPARATION AXIOMS
- 7. Compactness and Related Notions
- 8. Stronger Separation Axioms and Their Uses
PART III: CONNECTEDNESS & ALGEBRAIC TOPOLOGY
- 9. Connectedness: Fundamentals
- 10. Higher-Dimensional Connectedness
- 11. Highly Disconnected Spaces. Peano Curves
- 12. Paths in Topological and Metric Spaces
- 13. Homotopy and Fundamental Group
APPENDICES
- A. Background on Sets and Categories
- B. Fixed Point Theorems of Banach & Caristi
- C. Spectra of Commutative Rings
- D. More on Topological Groups
- E. Between Topology and Functional Analysis
- F. The Sequence Spaces l8(S)
- G. Topological Vector Spaces
What You Will Learn in Topology for the Working Mathematician
Topology for the Working Mathematician by Michael Müger is a modern and comprehensive textbook designed for graduate students and researchers in pure mathematics and mathematical physics. Serving as an essential advanced guide, this volume provides a robust framework for topology for the working mathematician problem solving practice.
The book systematically covers topological spaces, continuous mappings, metric spaces, compactness, connectedness, quotient spaces, fundamental groups, and elementary homotopy theory. By connecting abstract topological concepts directly with functional analysis and algebra, Müger enables readers to carry out essential topological space structure proofs with total analytical precision.
Treasured for its clarity, direct style, and focus on practical mathematical tools, this treatise remains a vital resource for modern analysts and geometers. Müger’s structured approach equips learners with analytical tools required for mastering modern topology principles across mathematical disciplines.
Book Details & Specifications
Title:
Topology for the Working Mathematician by Michael Müger
Publisher:
Radboud University
Year:
2022
Pages:
465
Type:
PDF
Language:
English
ISBN-10 #:
0131816292
ISBN-13 #:
978-0131816299
License:
External Educational Resource
Amazon:
Amazon
About the Author: Michael Muger
The author Michael Muger
is a Professor of Mathematics at Radboud University Nijmegen in the Netherlands, widely recognized for his research in operator algebras, category theory, quantum field theory, and topology.
Throughout his academic career, Professor Müger has dedicated himself to rigorous mathematical exposition, providing scholars with comprehensive advanced topology reference guides.
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