Theorems · Theorem · general topology

mem_closure_image

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y} {s : Set X}
  {x : X}, ContinuousAt f x → x ∈ closure s → f x ∈ closure (f '' s)

Defined in

Mathlib.Topology.Continuous

Cited by

1 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpace