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Theorems · Theorem · general topology

IsLocalHomeomorph.comap_discreteTopology

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  IsLocalHomeomorph f → ∀ [DiscreteTopology Y], DiscreteTopology X

A space that admits a local homeomorphism to a discrete space is itself discrete.

Defined in
Mathlib.Topology.IsLocalHomeomorph
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Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceDiscreteTopology
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TopologicalSpace · cited by 24529TopologicalSpaceDiscreteTopology · cited by 373DiscreteTopologyIsLocalHomeomorph · cited by 35IsLocalHomeomorphHomeomorph.Set.univ · cited by 16Set.univHomeomorph.discreteTopology_iff · cited by 7Homeomorph.discreteTopolo…IsLocalHomeomorph.isLocalHomeomorphOn · cited by 6IsLocalHomeomorph.isLocal…IsLocalHomeomorphOn.discreteTopology_of_image · cited by 3IsLocalHomeomorphOn.discr…IsLocalHomeomorph.comap_discr…CITED BYCITES

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