# hw1sol - 147 HW1 Solutions 2.13.1) Let X be a topological...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 147 HW1 Solutions 2.13.1) Let X be a topological space; let A be a subset of X . Suppose that for each x ∈ A there is an open set U containing x such that U ⊂ A . Show that A is open in X . Solution: Let x ∈ U x ⊂ A for each x ∈ A such that U x are all open. We know these sets, U x , exist by the problem statement. Then S x ∈ A U x = A , so A is open. 2.13.2) Consider the nine topologies on the set X = a,b,c indicated in Example one of § 12. Compare them; that is, for each pair of topologies, determine whether they are comparable, and if so, which is finer. Solution: 1 is coarser than all others. 2 is finer 1. 3 is finer than 1. 4 is finer than 1,3. 5 is finer than 1. 6 is finer than 1,2,3,4. 7 is finer than 1,2,3. 8 is finer than 1,2,3,7. 9 is finer than all others. 1 2.13.4) (a) If {T α } is a family of topologies on X , show that T T α is a topology on X . Is S T α a topology on X ?...
View Full Document

## This note was uploaded on 05/19/2010 for the course MAT mat147 taught by Professor Derekwise during the Spring '10 term at UC Davis.

### Page1 / 2

hw1sol - 147 HW1 Solutions 2.13.1) Let X be a topological...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online