Chapter 1: Topological Spaces

Question 1

Topological space

Answer 1

The set X together with a topology T on X

Question 2

Trivial topology

Answer 2

T={empty set, X}

Question 3

Discrete Topology

Answer 3

T= collection of all subsets of X

Question 4

Finite Complement Topology

Answer 4

T = empty set and every set in R with a finite complement

Question 5

Finer

Coarser

Answer 5

If T_1 is a subset of T_2 then T_2 is ______ than T_1 and T_1 is _____ than T_2

Question 6

A topology T on A set X is…

Answer 6

A collection of subsets of X, (open sets) such that:

1) empty set and X are open sets
2) the intersection of finitely many open sets is an open set
3) the Union of any collection of open sets is an open set