Theorems · Theorem · general topology
csSup_mem_closure
∀ {α : Type u_1} [inst : ConditionallyCompleteLinearOrder α] [inst_1 : TopologicalSpace α] [OrderTopology α]
{s : Set α}, s.Nonempty → BddAbove s → sSup s ∈ closure s- Defined in
- Mathlib.Topology.Order.Monotone
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 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
- OrderTopologystatement and proof · cited by 1,355
- closurestatement · cited by 1,254
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- isLUB_csSupproof · cited by 34
- IsLUB.mem_closureproof · cited by 6
Cited by4
Results whose statement or proof uses this declaration.
- Real.ediam_eqproof · cited by 4
- IsClosed.Icc_subset_of_forall_mem_nhdsGT_of_Icc_subsetproof · cited by 2
- Ordinal.mem_closure_tfaeproof · cited by 1
- Ordinal.enumOrd_isNormal_iff_isClosedproof · cited by 0