Introduction to Topology

ISBN-13: 9783110378153 / Angielski / Miękka / 2016 / 249 str.

Min Yan;Higher Education Press Ltd. Comp.

Opis

In this book, author uses knowledge from analysis course as a starting point and gradually builds up more abstract concepts in topology for students. Point set topology and combinatorial topology are arranged in alternating order to alleviate learning pressure and exercises are immersed into discussions. The introduction of a concept is followed by examples immediately, and then followed by relevant exercises to facilitate the learning process.

Spis treści

1 Set and Map
1.1 Set
1.2 Map
1.3 Counting
1.4 Equivalence Relation and Quotient
2.Metric Space
2.1 Metric
2.2 Ball
2.3 Open Subset
2.4 Continuity
2.5 Limit Point
2.6 Closed Subset
3.Graph and Network
3.1 Seven Bridges in KSnigsberg
3.2 Proof of One-Trip Criterion
3.3 Euler Formula
3.4 Application of Euler Formula
4 Topology
4.1 Topological Basis and Subbasis
4.2 Open Subset
4.3 Topological Space
4.4 Comparing Topologies
4.5 Limit Point and Closed Subset
4.6 Closure
5 Basic Topological Concepts
5.1 Continuity
5.2 Homeomorphism
5.3 Subspace
5.4 Product
5.5 Quotient
6. Complex
6.1 Simplicial Complex
6.2 CW-Complex
6.3 Projective Space
6.4 Euler Number
7 Topological Properties
7.1 Hausdorff Space
7.2 Connected Space
7.3 Path Connected Space
7.4 Connected Component
7.5 Compact Space
7.6 Limit Point Compact Space
8 Surface
8.1 Manifold
8.2 Surface
8.3 Simplicial Surface
8.4 Planar Diagram
8.5 Cut and Paste
8.6 Classification of Surface
8.7 Recognition of Surface
9 Topics in Point Set Topology
9.1 Normal Space
9.2 Paracompact Space
9.3 Complete Metric Space
9.4 Baire Category Theorem
9.5 Infinite Product
9.6 Space-Filling Curve
9.7 Space of Maps

O autorze

Min Yan, HongKong University of Science and Technology, HongKong.