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Theorems · Theorem · general topology

IsCompact.isLUB_sSup

∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [ClosedIciTopology α]
  {s : Set α}, IsCompact s → s.Nonempty → IsLUB s (sSup s)
Defined in
Mathlib.Topology.Order.Compact
Cited by
1 results in Mathlib
Foundations
Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
ConditionallyCompleteLinearOrderTopologicalSpaceClosedIciTopology
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousOn.isBigOWith_principal · cited by 1ContinuousOn.isBigOWith_p…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.Nonempty · cited by 2627Set.NonemptyIsCompact · cited by 1282IsCompactSupSet.sSup · cited by 954SupSet.sSupConditionallyCompleteLinearOrder · cited by 542ConditionallyCompleteLine…IsLUB · cited by 280IsLUBClosedIciTopology · cited by 156ClosedIciTopologyIsCompact.isGLB_sInf · cited by 3IsCompact.isGLB_sInfIsCompact.isLUB_sSupCITED BYCITES

Cites9

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Cited by1

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