- #1

Symmetryholic

- 18

- 0

## Homework Statement

Let [tex] A \subset X [/tex]; let [tex] f : A \rightarrow Y[/tex] be continuous; let Y be Hausdorff. Show that if f may be extended to a continuous function [tex]g: \overline{A} \rightarrow Y[/tex], then g is uniquely determined by f.

## Homework Equations

## The Attempt at a Solution

If f is a homeomorphism, we can say A is a Hausdorff space.

Just given a continuous function f, I am clueless how to start this problem.

Any advice will be appreciated.