Page 7 - DMTH503_TOPOLOGY

Richa Nandra, Lovely Professional University Unit 1: Topological Spaces

Unit 1: Topological Spaces Notes

CONTENTS
Objectives
Introduction

1.1 Topology and Different Kinds of Topologies
1.1.1 Topology
1.1.2 Different Kinds of Topologies

1.2 Intersection and Union of Topologies
1.3 Open Set, Closed Set and Closure of a Set
1.3.1 Definition of Open Set and Closed Set
1.3.2 Door Space
1.3.3 Closure of a Set

1.3.4 Properties of Closure of Sets
1.4 Neighborhood
1.5 Dense Set and Boundary Set

1.5.1 Dense Set and No where Dense
1.5.2 Boundary Set
1.6 Separable Space, Limit Point and Derived Set
1.6.1 Separable Space
1.6.2 Limit Point or Accumulation Point or Cluster Point

1.6.3 Derived Set
1.7 Interior and Exterior
1.7.1 Interior Point and Exterior Point

1.7.2 Interior Operator and Exterior Operator
1.7.3 Properties of Interior
1.7.4 Properties of Exterior
1.8 Summary
1.9 Keywords

1.10 Review Questions
1.11 Further Readings

Objectives

After studying this unit, you will be able to:

 Describe the concept of topological spaces;

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