Theorems · Theorem · general topology

IsConnected.preimage_of_isOpenMap

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : Set β},
  IsConnected s → ∀ {f : α → β}, Function.Injective f → IsOpenMap f → s ⊆ Set.range f → IsConnected (f ⁻¹' s)

Defined in

Mathlib.Topology.Connected.Basic

Cited by

2 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace