Recent content by edcvfr

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    Is the Intersection of a Compact Set and a Closed Set Always Compact?

    Thank you very much for helping me with this problem.
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    Is the Intersection of a Compact Set and a Closed Set Always Compact?

    could it be more specific? To me it is comprehensive enough.
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    Is the Intersection of a Compact Set and a Closed Set Always Compact?

    Alright, I tried to think by your hints and get some results. I'm not sure my explanation is correct. Please correct it for me: Call G the finite set of open subcover of E, A' be an open cover of A. If we union A' and complement of F and call it M (open because F is closed), we still have an...
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    Is the Intersection of a Compact Set and a Closed Set Always Compact?

    Sorry canis, I'm afraid I don't get your idea. Can you please elaborate on that? I apologize for my stupidity.
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    Is the Intersection of a Compact Set and a Closed Set Always Compact?

    I thought about your idea before. I got this far: F is closed. Call {Gi} class of sets such that F\subset\bigcupiGi and {Hi} class of sets such that E\subset\bigcupiHi. Because E is compact, H has finite number of subcovers. If we union G and H, we have open cover that covers both E, F and...
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    Is the Intersection of a Compact Set and a Closed Set Always Compact?

    Homework Statement E is a compact set, F is a closed set. Prove that intersection of E and F is compact Homework Equations The Attempt at a Solution On Hausdoff space (the most general space I can work this out), compact set is closed. So E is closed. So intersection of E and F is...