Theorems · Theorem · general topology

Topology.IsCoinducing.locallyConnectedSpace

∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [LocallyConnectedSpace α] [inst_2 : TopologicalSpace β]
  {f : α → β}, Topology.IsCoinducing f → LocallyConnectedSpace β

Any topology coinduced by a locally connected topology is locally connected.

Defined in

Mathlib.Topology.Connected.LocallyConnected

Cited by

1 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceLocallyConnectedSpaceTopologicalSpace