I know that every Hausdorff space $X$ has the following property:
$A\subset X$ is compact $\Rightarrow A$ is closed
In other words, that is necessary for $X$ to be Hausdorff. But is it sufficient? If not, what information can get from this property?
I know that every Hausdorff space $X$ has the following property:
$A\subset X$ is compact $\Rightarrow A$ is closed
In other words, that is necessary for $X$ to be Hausdorff. But is it sufficient? If not, what information can get from this property?
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