Theorems · Theorem · general topology

map_mem_closure

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

Defined in

Mathlib.Topology.Continuous

Cited by

4 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace