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- #1

- Mar 10, 2012

- 834

I tried to construct an open subset $K$ of $U$ such that $\overline{K} \subseteq U$ and $x \in K$. Since if this happens then $C=\overline{K}$ and $V=K$ do the job. But I have not been able to. I found a proof over the internet using "one point compactification" but this concept is not discussed in my book..so there must be another way. Please help.