Theorems · Theorem · general topology

Dense.sdiff_singleton

∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s : Set X},
  Dense s → ∀ (x : X) [(nhdsWithin x {x}ᶜ).NeBot], Dense (s \ {x})

Removing a non-isolated point from a dense set, one still obtains a dense set.

Defined in

Mathlib.Topology.Separation.Basic

Cited by

2 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT1SpaceFilter.NeBot