Theorems · Theorem · general topology

Set.MapsTo.closure

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X}
  {t : Set Y}, Set.MapsTo f s t → Continuous f → Set.MapsTo f (closure s) (closure t)

If a continuous map f maps s to t, then it maps closure s to closure t.

Defined in

Mathlib.Topology.Continuous

Cited by

10 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace