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Functions agreeing on dense sets: weakest separation axiom

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#general-topology #continuity #separation-axioms
54
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Is {x : ϕ(x)} a set with ϕ(x) being the property: ∀y (x ∈ y)

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#elementary-set-theory #separation-axioms
169
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Is the set of all the subsets of a completely separable space still completely separable?

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#general-topology #separation-axioms #separable-spaces
158
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$T_1$-space with compact dense subset

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#general-topology #compactness #separation-axioms
347
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A regular, non-Hausdorff, non-normal space

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#general-topology #examples-counterexamples #separation-axioms
167
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Separating closed sets by clopen sets in $\omega_1$.

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#general-topology #separation-axioms
284
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Completely Regular space and the topology $\tau_A$

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#general-topology #functions #continuity #separation-axioms
50
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Canonical example of non-Hausdorff Ellis group

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#dynamical-systems #separation-axioms
425
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Showing that intersection of arbitrarily many compact sets in Hausdorff space is compact.

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#general-topology #compactness #separation-axioms
104
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$R_0$ space with Hausdorff quotient

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#general-topology #terminology #separation-axioms
880
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Example of a compact subset that is not closed

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#general-topology #compactness #separation-axioms
1.9k
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If product space of two spaces is normal, then are the two spaces normal?

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#general-topology #separation-axioms
37
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A space $X$ with property that all compact subspaces are closed.

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#general-topology #compactness #separation-axioms
1.8k
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A confusion regarding proof of "Every regular second countable space is normal", given in Munkres

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#general-topology #separation-axioms
73
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Finding a topology doesn't convey Hausdorff property by an injective continuous function

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#general-topology #continuity #separation-axioms

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