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The point set $M$ is said to be perfectly compact if and only if it is true that if $G$ is a monotonic collection of non-empty subsets of $M$ then there is a point $p$ that is a point or a limit point of every every element of $G$.

We are allowed to assume that X is Hausdorff and at most (if we need it) metric.

This is my first time seeing "perfectly compact"... do you approach this using contradiction? Assume that X is not compact (i.e. there is a cover with no finite sub cover) to give a contradiction?

**Problem:**If $X$ is perfectly compact and has a countable basis, then $X$ is compact.We are allowed to assume that X is Hausdorff and at most (if we need it) metric.

This is my first time seeing "perfectly compact"... do you approach this using contradiction? Assume that X is not compact (i.e. there is a cover with no finite sub cover) to give a contradiction?

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