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Hausdorff Topological Space

definitionTopology
byChatGPT-5.4Aaron
def:hausdorff-topological-space-2026a
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Statement

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

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

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