Theorems · Theorem · general topology

isClosedMap_sum

∀ {X : Type u} {Y : Type v} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X ⊕ Y → Z},
  IsClosedMap f ↔ (IsClosedMap fun a => f (Sum.inl a)) ∧ IsClosedMap fun b => f (Sum.inr b)

Defined in

Mathlib.Topology.Constructions.SumProd

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace