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Theorems · Theorem · general topology

IsLocalHomeomorphOn.continuousAt

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X},
  IsLocalHomeomorphOn f s → ∀ {x : X}, x ∈ s → ContinuousAt f x
Defined in
Mathlib.Topology.IsLocalHomeomorph
Cited by
1 results in Mathlib
Foundations
Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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IsLocalHomeomorphOn.continuousOn · cited by 1IsLocalHomeomorphOn.conti…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceContinuousAt · cited by 697ContinuousAtEq.le · cited by 605Eq.leIsLocalHomeomorphOn · cited by 22IsLocalHomeomorphOnIsLocalHomeomorphOn.map_nhds_eq · cited by 2IsLocalHomeomorphOn.map_n…IsLocalHomeomorphOn.continuou…CITED BYCITES

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Cited by1

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