Theorems · Theorem · general topology

continuousAt_update_of_ne

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [T1Space X] [inst_2 : DecidableEq X]
  [inst_3 : TopologicalSpace Y] {f : X → Y} {x x' : X} {y : Y},
  x' ≠ x → (ContinuousAt (Function.update f x y) x' ↔ ContinuousAt f x')

Defined in

Mathlib.Topology.Separation.Basic

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceT1SpaceDecidableEqTopologicalSpace