初心者のための一般位相幾何学（テキスト） General Topology for Beginners

Mehta, Jay

Cambridge University Press（2026/02発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 350 p.
• 言語 ENG
• 商品コード 9781009505888
• DDC分類 514

Full Description

This textbook focuses on general topology. Meant for graduate and senior undergraduate mathematics students, it introduces topology thoroughly from scratch and assumes minimal basic knowledge of real analysis and metric spaces. It begins with thought-provoking questions to encourage students to learn about topology and how it is related to, yet different from, geometry. Using concepts from real analysis and metric spaces, the definition of topology is introduced along with its motivation and importance. The text covers all the topics of topology, including homeomorphism, subspace topology, weak topology, product topology, quotient topology, coproduct topology, order topology, metric topology, and topological properties such as countability axioms, separation axioms, compactness, and connectedness. It also helps to understand the significance of various topological properties in classifying topological spaces.

Contents

1. Preliminaries; 2. Topological Spaces 3. Continuous Functions; 4. Techniques of Creating Topologies: New from Old; 5. The Topology of Metric Spaces; 6. Countability Axioms; 7. Separation Axioms; 8. Compactness; 9. Connectedness; Appendix: From General Topology to Algebraic Topology; References; Index.