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Theorems · Theorem · general topology

dense_compl_singleton

∀ {X : Type u} [inst : TopologicalSpace X] (x : X) [(nhdsWithin x {x}ᶜ).NeBot], Dense {x}ᶜ

If x is not an isolated point of a topological space, then {x}ᶜ is dense in the whole space.

Defined in
Mathlib.Topology.ClusterPt
Cited by
6 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceFilter.NeBot

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Cited by6

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