It is a fact that if X is a compact topoloical space then a closed subspace of X is compact.(adsbygoogle = window.adsbygoogle || []).push({});

Is an open subspace G of X also compact?

please consider the following and note if i am wrong;

proof: Since G is open then the relative topology on G is class {H_i}of open subset of X such that the union of all sets in this class is G. but X is compact and each H_i is the intersection of G with P_i for corresponding i. The result foolow from the fact {p_i} has a finite subclass which contains X.

hence every open subspace of a compact space is compact.

pls, am i right?

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# Open subspace of a compact space

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