Topology for the Working Mathematician by Michael Muger

Book Contents :-
PART I: FUNDAMENTALS 1. Introduction 2. Basic Notions of Point-Set Topology 3. Metric Spaces: Completeness and Its Applications 4. More Basic Topology 5. Convergence and Continuity 6. New Spaces from Old PART II: COVERING AND SEPARATION AXIOMS (BEYOND T2) 7. Compactness and Related Notions 8. Stronger Separation Axioms and Their Uses PART III: CONNECTEDNESS. STEPS TOWARDS ALGEBRAIC TOPOLOGY 9. Connectedness: Fundamentals 10. Higher-Dimensional Connectedness 11. Highly Disconnected Spaces. Peano Curves 12. Paths in Topological and Metric Spaces 13. Homotopy. The Fundamental Group(oid). Coverings A. Background on Sets and Categories B. The Fixed Point Theorems of Banach and Caristi C. Spectra of Commutative Rings. Spectral Spaces D. More on Topological Groups E. Between Topology and Functional Analysis: C0(X, F) F. The Sequence Spaces l?(S) G. Topological Vector Spaces (Mostly Normed)

About this book :-
"Topology for the Working Mathematician" by Michael Müger is a "beginner-friendly" yet rigorous introduction to "topology" aimed at students and practicing mathematicians. It focuses on core concepts such as "topological spaces", "continuity", and convergence, providing clear explanations that connect abstract ideas to practical mathematical use. The book emphasizes understanding the foundational tools of topology that are widely applied across various fields of mathematics. The text covers essential topics in "general topology", including open and closed sets, continuous functions, metric spaces, and limit points. It also introduces important constructions like product and quotient topologies and discusses properties such as compactness and connectedness. Each topic is presented with examples and exercises designed to develop intuition and strengthen comprehension, making complex concepts more approachable for readers at different levels of experience. Michael Müger’s book is ideal for both self-study and classroom use. With its structured explanations, step-by-step examples, and focus on practical applications, "Topology for the Working Mathematician" equips readers with the tools to understand and use topology in real mathematical contexts. By the end, students gain a solid foundation in "topology", confidence in handling "continuous functions", and readiness for advanced study in mathematics.

Book Detail :-
Title: Topology for the Working Mathematician by Michael Muger
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 Author :-
The author Michael Muger is a mathematician and "Associate Professor" at Radboud University Nijmegen, specializing in "topology", operator algebras, and category theory. His research connects abstract mathematics with applications in mathematical physics, making complex concepts accessible for students and researchers alike. His book, "Topology for the Working Mathematician", is designed for graduate and advanced undergraduate students, providing a practical approach to "general topology".

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