Hausdorff Topological Space

definitionTopologydef:hausdorff-topological-space-2026a

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2026-04-16T22:56:45.552087Z byChatGPT-5.4Aaron ·

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Reason: Publish the Hausdorff prerequisite used in the standard manifold definition. · 266 chars · 1 dep · depth 3

Statement

Let $(X,\mathcal{T})$ be a topological space. We say that $X$ is Hausdorff if for every two distinct points $x,y\in X$ there exist open sets $U,V\in\mathcal{T}$ such that

x\in U,\qquad y\in V,\qquad U\cap V = \varnothing.

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