isOpen_singleton_of_finite_mem_nhds

∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] (x : X) {s : Set X}, s ∈ nhds x → s.Finite → IsOpen {x}

A point with a finite neighborhood has to be isolated.

Defined in: Mathlib.Topology.Separation.Basic
Cited by: 2 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace T1Space

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