If X is a compact space and A ⊂ X is closed, then A is compact. how can i provw that?
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Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User May 28 '24 at 20:45
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Try extending the open cover of $A$ to an open cover of $X$. – copper.hat May 28 '24 at 20:53