Theorems · Theorem · general topology

completelyRegularSpace_iff_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

2 results in Mathlib

Foundations

Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpace