# Closed set in a compact set

1. Dec 10, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
Let X be a topological space. Let A be compact in X. Let B be contained in A. Let B also be closed in X. Is it always true that B is compact in X?

2. Relevant equations

3. The attempt at a solution

2. Dec 10, 2007

### morphism

B will be compact in A, and consequently in X as well.

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