(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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.

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# Homework Help: A continuous function in Hausdorff space

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