Theorems · Definition · general topology

Equiv.toHomeomorphOfDiscrete

{X : Type u_1} →
  {Y : Type u_2} →
    [inst : TopologicalSpace X] →
      [inst_1 : TopologicalSpace Y] → [DiscreteTopology X] → [DiscreteTopology Y] → X ≃ Y → X ≃ₜ Y

Any bijection between discrete spaces is a homeomorphism.

Defined in

Mathlib.Topology.Homeomorph.Defs

Cited by

3 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceDiscreteTopologyDiscreteTopology