Theorems · Theorem · general topology
TopologicalSpace.Opens.mem_sSup
∀ {α : Type u_2} [inst : TopologicalSpace α] {Us : Set (TopologicalSpace.Opens α)} {x : α},
x ∈ sSup Us ↔ ∃ u ∈ Us, x ∈ u- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- SupSet.sSupstatement · cited by 954
- sSup_eq_iSupproof · cited by 42
Cited by6
Results whose statement or proof uses this declaration.
- TopologicalSpace.Opens.isBasis_iff_coverproof · cited by 4
- Topology.IsInducing.map_functorObjproof · cited by 1
- IsOpenMap.exists_opens_image_eq_of_prespectralSpaceproof · cited by 1
- ProjectiveSpectrum.basicOpen_eq_union_of_projectionproof · cited by 1
- AlgebraicGeometry.Scheme.RationalMap.mem_domainproof · cited by 0
- Topology.IsInducing.le_functorObj_iffproof · cited by 0