Theorems · Theorem · algebraic topology

IsEvenlyCovered.of_preimage_eq_empty

∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} (I : Type u_3)
  [inst_2 : TopologicalSpace I] [IsEmpty I] {x : X} {U : Set X}, U ∈ nhds x → f ⁻¹' U = ∅ → IsEvenlyCovered f x I

Defined in

Mathlib.Topology.Covering.Basic

Cited by

4 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceIsEmpty