Theorems · Definition · general topology

Homeomorph.sumProdDistrib

{X : Type u} →
  {Y : Type v} →
    {Z : Type u_2} →
      [inst : TopologicalSpace X] →
        [inst_1 : TopologicalSpace Y] → [inst_2 : TopologicalSpace Z] → (X ⊕ Y) × Z ≃ₜ X × Z ⊕ Y × Z

(X ⊕ Y) × Z is homeomorphic to X × Z ⊕ Y × Z.

Defined in: Mathlib.Topology.Constructions.SumProd
Cited by: 2 results in Mathlib
Foundations: Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace TopologicalSpace

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Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

TopologicalSpacestatement and proof · cited by 24,529
Equiv.symmproof · cited by 3,681
Homeomorphstatement · cited by 725
Homeomorph.symmproof · cited by 365
Equiv.sumProdDistribproof · cited by 11
Equiv.toHomeomorphOfContinuousOpenproof · cited by 5

Cited by3

Results whose statement or proof uses this declaration.

Homeomorph.sumProdDistrib_symm_applystatement and proof · cited by 0
Homeomorph.prodSumDistribproof · cited by 0
Homeomorph.sumProdDistrib_applystatement and proof · cited by 0