Theorems · Theorem · general topology

continuousWithinAt_sdiff_singleton

∀ {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 (s \ {y}) x ↔ ContinuousWithinAt f s x

See also continuousWithinAt_sdiff_self for the case y = x but not requiring T1Space.

Defined in

Mathlib.Topology.Separation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT1Space