Theorems · Theorem · general topology
isOpen_univ
∀ {X : Type u} [inst : TopologicalSpace X], IsOpen Set.univ- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 112 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 7 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- IsOpenstatement · cited by 2,400
- TopologicalSpace.isOpen_univproof · cited by 1
Cited by123
Results whose statement or proof uses this declaration.
- nhds_basis_opensproof · cited by 54
- Homeomorph.toOpenPartialHomeomorphproof · cited by 28
- interior_univproof · cited by 24
- Bundle.Trivial.trivializationproof · cited by 17
- Topology.IsOpenEmbedding.toOpenPartialHomeomorphproof · cited by 14
- IsClosed.isLocallyClosedproof · cited by 12
- IsOpenMap.isOpen_rangeproof · cited by 11
- uniqueMDiffOn_univproof · cited by 10
- AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
- AlgebraicGeometry.QuasiCompact.compactSpace_of_compactSpaceproof · cited by 7
- Topology.IsConstructible.isLocallyConstructibleproof · cited by 7
- isOpen_pi_iffproof · cited by 6