Theorems · Theorem · general topology

Topology.IsQuotientMap.secondCountableTopology

∀ {X : Type u_1} [inst : TopologicalSpace X] {Y : Type u_2} [inst_1 : TopologicalSpace Y] {π : X → Y}
  [SecondCountableTopology X], Topology.IsQuotientMap π → IsOpenMap π → SecondCountableTopology Y

A second countable space is mapped by an open quotient map to a second countable space.

Defined in

Mathlib.Topology.Bases

Cited by

1 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceSecondCountableTopology