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Theorems · Theorem · general topology

Prod.noncompactSpace_iff

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y],
  NoncompactSpace (X × Y) ↔ NoncompactSpace X ∧ Nonempty Y ∨ Nonempty X ∧ NoncompactSpace Y
Defined in
Mathlib.Topology.Compactness.Compact
Cited by
0 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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TopologicalSpace · cited by 24529TopologicalSpaceFilter.NeBot · cited by 853Filter.NeBotFilter.cocompact · cited by 141Filter.cocompactNoncompactSpace · cited by 21NoncompactSpaceProd.noncompactSpace_iffCITED BYCITES

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