Theorems · Theorem · general topology

extendFrom_eq

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T2Space Y] {A : Set X}
  {f : X → Y} {x : X} {y : Y}, x ∈ closure A → Filter.Tendsto f (nhdsWithin x A) (nhds y) → extendFrom A f x = y

Defined in

Mathlib.Topology.ExtendFrom

Cited by

5 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceT2Space