- #1

qinglong.1397

- 108

- 1

## Homework Statement

Suppose X = A[tex]\cup[/tex]B where A and B are closed sets. Suppose f : (X, T

_{X}) [tex]\rightarrow[/tex] (Y, T

_{Y}) is a map such that f|

_{A}and

f|

_{B }are continuous (where A and B have their subspace topologies). Show that f is continuous. What happens if A and B

are open? What happens if A or B is neither open nor closed?

T

_{X}means the topology on set X; T

_{Y}the topology on Y. f|

_{A}means the restriction of f on A; f|

_{B}the restriction on B.

## Homework Equations

## The Attempt at a Solution

I do not know how to prove, so is there anyone who can give me the answer? Thank you very much!