Proof: $X$ is Hausdorff if and only if the diagonal $\Delta$ is closed in $X\times X$.
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$X$ is Hausdorff if and only if the diagonal of $X\times X$ is closed
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$X$ compact Hausdorff space, characterize the maximal ideals of $C(X)$
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G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
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Let $(X, \mathcal{T})$ be a metrizable space. Prove that $X$ Lindelöf implies that $X$ is separable.
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Proof concerning regular space: there exist a closed set contained in any open set containing $x$
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Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
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Prove that an open interval and a closed interval are not homeomorphic
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
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Cantor diagonalization and fundamental theorem
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How big can a separable Hausdorff space be?
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$\|h(x)-h(y)\|\geq 3\|x-y\|$ prove that image of open is open
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Proof Verification: Let $D=\{ \frac{1}{n} \mid n\in\mathbb{N} \} \cup\{0\} \subset \mathbb{E}^1$. Prove that $D$ is compact.
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Disjoint compact sets in a Hausdorff space can be separated
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Real projective space is Hausdorff: is this proof correct?
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Proving $|S \times \mathbb{N}|=|S|$ when $S$ is an infinite set
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Open subspaces of locally compact Hausdorff spaces are locally compact
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Let $B\subset\mathbb{R}^d$ be closed and $z\in\mathbb{R}^d$, show that there is $b_0\in B$ such that $\delta(z,B)=\|z-b_0\|$.