Topology 2E : First Course - MUNKRES, JAMES R.

Topology 2E : First Course

JAMES R. MUNKRES

Yayınevi: Pearson Education

Yayın tarihi: 12/1999

ISBN: 9780131816299

Ciltli | İngilizce | 560 Sayfa |

Tür: Matematik-İstatistik

For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.

*Follows the present-day trend of exploring the subject much more extensively with one semester devoted to general topology and a second to algebraic topology. *Exercises - Varied in difficulty from the routine to the challenging. Supplementary exercises at the end of several chapters explore additional topics.

*Deepen students' understanding of concepts and theorems just presented rather than simply test comprehension.

Table of Contents
*I. GENERAL TOPOLOGY
*Set Theory and Logic
*Topological Spaces and Continuous Functions
*Connectedness and Compactness
*Countability and Separation Axioms
*The Tychonoff Theorem
*Metrization Theorems and Paracompactness
*Complete Metric Spaces and Function Spaces
*Baire Spaces and Dimension Theory
*II. ALGEBRAIC TOPOLOGY
*The Fundamental Group
*Separation Theorems
*The Seifert-van Kampen Theorem
*Classification of Surfaces
*Classification of Covering Spaces
*Applications to Group Theory

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