Theorems · Theorem · general topology
IsCompact.sInf_mem
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [ClosedIicTopology α]
{s : Set α}, IsCompact s → s.Nonempty → sInf s ∈ s- Defined in
- Mathlib.Topology.Order.Compact
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.Nonemptystatement and proof · cited by 2,627
- IsCompactstatement and proof · cited by 1,282
- InfSet.sInfstatement and proof · cited by 935
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- IsLeastproof · cited by 122
- ClosedIicTopologystatement and proof · cited by 115
- IsCompact.exists_isLeastproof · cited by 9
- IsLeast.csInf_memproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- IsCompact.exists_sInf_image_eq_and_leproof · cited by 2
- IsCompact.isLeast_sInfproof · cited by 2
- locallyIntegrableOn_mul_sum_Iccproof · cited by 2
- ContinuousOn.isBigOWith_rev_principalproof · cited by 1
- IsCompact.sSup_memproof · cited by 0