List questions from separation-axioms

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Seeking counterexample or proof for equivalence of two separation properties

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coarsest topology for separation axioms

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show that a perfectly normal space is completely normal

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Normal space- equivalent condition: $\forall U, V$ - open $: U \cup V = X \ \ \ \exists F \subset U \ , G \subset V$ - closed $: F \cup G = X$

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$X$ - regular, $A \subset X$ - closed $\Rightarrow \ \ X/A$ - quotient space is Hausdorff

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List Question

Showing $\mathbb{R}/\mathbb{Q}$ is not Hausdorff

Seeking counterexample or proof for equivalence of two separation properties

coarsest topology for separation axioms

show that a perfectly normal space is completely normal

Normal space- equivalent condition: $\forall U, V$ - open $: U \cup V = X \ \ \ \exists F \subset U \ , G \subset V$ - closed $: F \cup G = X$

Hausdorff space in which each point has a compact neighbourhood is locally compact

Separation axioms in uniform spaces

$X$ - regular, $A \subset X$ - closed $\Rightarrow \ \ X/A$ - quotient space is Hausdorff

The product of Hausdorff spaces is Hausdorff

Converting between $T_1$ and $T_2$

Non-T1 Space: Is the set of limit points closed?

If $X$ is Hausdorff then every finite set is closed.

Equivalence of different definitions of "monotonically normal space."

Hausdorff spaces from continuous functions

Finite subsets of Hausdorff spaces

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