S.No.

Content of the topics

Learning Objectives

Teaching Guidelines

Methodology

Time (Hours)

1

 Statements only of (Axiom of choice, Zorn’s Lemma, Well ordering theorem and Continuum hypothesis)

Students will be able to study of basics of topology 
Lecture should be effective so that student will be able to grasp the topics easily

Assignments/ Seminars/ Class Tests/ Presentations

10

 Definition and examples of topological spaces

 Neighbourhoods, Interior point and interior of a set

 Closed set as a complement of an open set

 Adherent point and limit point of a set,Closure of a set,Derived set

 Properties of closure operator, Boundary of a set, Dense subsets,Interior,Exterior and boundary operators

 Base and subbase for a topology

 Neighbourhood system of a point and its properties

 Basefor Neighbourhood system

 Relative(Induced) topology

 Alternative methods of defining a topolgy in terms of neighbourhood system and Kuratowski closure operator

 Comparison of topologies on a set,Intersection and union of topologies on a set

2


Student will be able to study of continuous functions and connectedness 
Lecture should be effective so that student will be able to grasp the topics easily

Assignments/ Seminars/ Class Tests/ Presentations

15

 Open and closed functions


 Connected and its characterization

 Connected subsets and their properties

 Continuity and connectedness



3

 Compact spaces and subsets

Student will be able to Study the compactness 
Lecture should be effective so that student will be able to grasp the topics easily

Assignments/ Seminars/ Class Tests/ Presentations

15

 Compactness in terms of finite intersection property

 Continuity and compact sets

 Basic properties of compactness

 Closedness of compactsubset and a continuous map from a compact space into a Hausdorff and its consequence

 Sequentially and countably compact sets

 Local compactness and one point compatification

4

 First countable, Second countable and separable spaces

Student will be able to know about the countable spaces 
Lecture should be effective so that student will be able to grasp the topics easily

Assignments/ Seminars/ Class Tests/ Presentations

12

 Hereditary and topological property

 Countability of a collection of disjoint open sets in separable and second countable spaces


 T0,T1,T2(Hausdorff) separation axioms, their characterization and basic properties
