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Theorems · Theorem · general topology

ContinuousWithinAt.insert

∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α}
  {x : α}, ContinuousWithinAt f s x → ContinuousWithinAt f (insert x s) x

Alias of the reverse direction of continuousWithinAt_insert_self.

Defined in
Mathlib.Topology.ContinuousOn
Cited by
1 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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hasMFDerivWithinAt_insert · cited by 3hasMFDerivWithinAt_insertSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceContinuousWithinAt · cited by 512ContinuousWithinAtcontinuousWithinAt_insert_self · cited by 5continuousWithinAt_insert…ContinuousWithinAt.insertCITED BYCITES

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Cited by1

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