Theorems · Theorem · general topology

TopologicalSpace.IsTopologicalBasis.isQuotientMap

∀ {X : Type u_1} [inst : TopologicalSpace X] {Y : Type u_2} [inst_1 : TopologicalSpace Y] {π : X → Y} {V : Set (Set X)},
  TopologicalSpace.IsTopologicalBasis V →
    Topology.IsQuotientMap π → IsOpenMap π → TopologicalSpace.IsTopologicalBasis (Set.image π '' V)

The image of a topological basis under an open quotient map is a topological basis.

Defined in

Mathlib.Topology.Bases

Cited by

2 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace