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Theorems · Theorem · general topology

QuasiSeparatedSpace.inter_isCompact

∀ {α : Type u_3} {inst : TopologicalSpace α} [self : QuasiSeparatedSpace α] (U V : Set α),
  IsOpen U → IsCompact U → IsOpen V → IsCompact V → IsCompact (U ∩ V)

The intersection of two open compact subsets of a quasi-separated space is compact.

Defined in
Mathlib.Topology.QuasiSeparated
Cited by
1 results in Mathlib
Foundations
Depth 50 from the axioms · uses propext, Quot.sound
Assumes
QuasiSeparatedSpace
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Around this declaration

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IsCompact.inter_of_isOpen · cited by 3IsCompact.inter_of_isOpenSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceIsOpen · cited by 2400IsOpenIsCompact · cited by 1282IsCompactQuasiSeparatedSpace · cited by 49QuasiSeparatedSpaceQuasiSeparatedSpace.inter_isC…CITED BYCITES

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Cited by1

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