Theorems · Theorem · general topology

Set.MapsTo.closure_left

∀ {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 → IsClosed t → Set.MapsTo f (closure s) t

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

Defined in

Mathlib.Topology.Continuous

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace