Theorems · Theorem · general topology

TopologicalSpace.IsOpenCover.comap

∀ {κ : Type u_2} {X : Type u_3} {Y : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  {v : κ → TopologicalSpace.Opens Y},
  TopologicalSpace.IsOpenCover v →
    ∀ (f : C(X, Y)), TopologicalSpace.IsOpenCover fun k => (TopologicalSpace.Opens.comap f) (v k)

Pullback of a covering of Y by a continuous map X → Y, giving a covering of X with the same index type.

Defined in

Mathlib.Topology.Sets.OpenCover

Cited by

4 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpace