Theorems · Definition · general topology

Homeomorph.sigmaProdDistrib

{Y : Type u_2} →
  [inst : TopologicalSpace Y] →
    {ι : Type u_7} →
      {X : ι → Type u_8} → [inst_1 : (i : ι) → TopologicalSpace (X i)] → ((i : ι) × X i) × Y ≃ₜ (i : ι) × X i × Y

(Σ i, X i) × Y is homeomorphic to Σ i, (X i × Y).

Defined in: Mathlib.Topology.Homeomorph.Lemmas
Cited by: 3 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: 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.toHomeomorphOfContinuousOpenproof · cited by 5
Equiv.sigmaProdDistribproof · cited by 3

Cited by3

Results whose statement or proof uses this declaration.

Homeomorph.toEquiv_sigmaProdDistribstatement and proof · cited by 0
Homeomorph.sigmaProdDistrib_applystatement and proof · cited by 0
Homeomorph.sigmaProdDistrib_symm_applystatement and proof · cited by 0