MCS 451, Topology (4 0 4)
Weeks

Course Topics

1

Introduction; Sets, Relations, Ordering, Partial Ordering

2

Topological spaces; definitions, accumulation points, closure of a set, interior, exterior and boundary, convergent sequences, coarser and finer topologies 
3

Basis and Sub bases, metric topologies

4

Topologies generated by classes of sets

5

Continuous and closed functions, homeomorphisms

6

The identification Topology and Quotient spaces

7

Separation axioms; T_{1 }spaces, Hausdorff spaces, Regular spaces,

8

Normal spaces, Urysohn's lemma, completely regular spaces

9

Compactness; covers, compactness and Hausdorff spaces, sequentially compact sets, local compactness

10

Connectedness

11

Complete metric spaces

12

Normed and function spaces, Ascoli’s theorem

13

Nets and Filters 
14

Review
