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Theorems · Theorem · general topology

IsCompact.exists_isGLB

∀ {α : Type u_2} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [ClosedIicTopology α] {s : Set α},
  IsCompact s → s.Nonempty → ∃ x ∈ s, IsGLB s x
Defined in
Mathlib.Topology.Order.Compact
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderTopologicalSpaceClosedIicTopology
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Around this declaration

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

IsCompact.exists_isLUB · cited by 0IsCompact.exists_isLUBSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceLinearOrder · cited by 8572LinearOrderSet.Nonempty · cited by 2627Set.NonemptyIsCompact · cited by 1282IsCompactIsGLB · cited by 213IsGLBIsLeast · cited by 122IsLeastClosedIicTopology · cited by 115ClosedIicTopologyIsLeast.isGLB · cited by 23IsLeast.isGLBIsCompact.exists_isLeast · cited by 9IsCompact.exists_isLeastIsCompact.exists_isGLBCITED BYCITES

Cites10

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Cited by1

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