Theorems · Theorem · general topology

CompletelyRegularSpace.completely_regular_isOpen

∀ {X : Type u} [inst : TopologicalSpace X] [CompletelyRegularSpace X] (x : X) (K : Set X),
  IsOpen K → x ∈ K → ∃ f, Continuous f ∧ f x = 0 ∧ Set.EqOn f 1 Kᶜ

Defined in

Mathlib.Topology.Separation.CompletelyRegular

Cited by

3 results in Mathlib

Foundations

Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceCompletelyRegularSpace