Theorems · Theorem · general topology

TopologicalSpace.IsTopologicalBasis.exists_mem_of_ne

∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {b : Set (Set X)},
  TopologicalSpace.IsTopologicalBasis b → ∀ {x y : X}, x ≠ y → ∃ a ∈ b, x ∈ a ∧ y ∉ a

Defined in

Mathlib.Topology.Separation.Basic

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT1Space