K is subset of complex plane. K is compact set and A is closed subset of K then A is compact set.
How to prove this problem??
I know definition of compact set, but i'm not use definition to problem.
2026-04-26 08:39:34.1777192774
Compact set of closed subset problem
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Let $\{U_a: a\in A\}$ a family of open sets in $K$ with $A\subset \bigcup \{U_a:a\in A\}$, then $\{U_a: a\in A\} \cup \{K-A\}$ is an open covering of $K$. It has a finite subcollection that covers $K$, so by discarding $K-A$ from the latter if necessary, we obtain a finite subcovering of $A$.