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Theorems · Theorem · general topology

ContinuousWithinAt.of_insert

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T1Space X] {x y : X}
  {s : Set X} {f : X → Y}, ContinuousWithinAt f (insert y s) x → ContinuousWithinAt f s x

Alias of the forward direction of continuousWithinAt_insert.

Defined in
Mathlib.Topology.Separation.Basic
Cited by
0 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceT1Space
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Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceContinuousWithinAt · cited by 512ContinuousWithinAtT1Space · cited by 275T1SpacecontinuousWithinAt_insert · cited by 3continuousWithinAt_insertContinuousWithinAt.of_insertCITED BYCITES

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