Theorems · Theorem · general topology
IsGLB.mem_closure
∀ {α : Type u_1} [inst : TopologicalSpace α] [inst_1 : LinearOrder α] [OrderTopology α] {a : α} {s : Set α},
IsGLB s a → s.Nonempty → a ∈ closure s- Defined in
- Mathlib.Topology.Order.IsLUB
- Cited by
- 5 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.
Cites9
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
- LinearOrderstatement and proof · cited by 8,572
- Set.Nonemptystatement and proof · cited by 2,627
- OrderTopologystatement and proof · cited by 1,355
- closurestatement · cited by 1,254
- IsGLBstatement and proof · cited by 213
- Filter.Frequently.mem_closureproof · cited by 5
- IsGLB.frequently_nhds_memproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- closure_Iooproof · cited by 20
- closure_Ioi'proof · cited by 5
- IsGLB.mem_of_isClosedproof · cited by 4
- csInf_mem_closureproof · cited by 1
- sInf_mem_closureproof · cited by 0