isCompactSystem_isCompact_isClosed

∀ (α : Type u_2) [inst : TopologicalSpace α], IsCompactSystem {s | IsCompact s ∧ IsClosed s}

The set of compact and closed sets is a compact system.

Defined in: Mathlib.Topology.Compactness.CompactSystem
Cited by: 2 results in Mathlib
Foundations: Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace

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

Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Set.ofPredstatement and proof · cited by 6,101
Set.Nonemptyproof · cited by 2,627
IsClosedstatement and proof · cited by 1,639
IsCompactstatement and proof · cited by 1,282
Set.dissipateproof · cited by 24
isClosed_biInterproof · cited by 16
IsCompactSystemstatement · cited by 15
IsCompact.nonempty_iInter_of_sequence_nonempty_isCompact_isClosedproof · cited by 4
Set.antitone_dissipateproof · cited by 4
IsCompactSystem.of_nonempty_iInterproof · cited by 2

Results whose statement or proof uses this declaration.