Theorems · Theorem · general topology
IsOpen.inter
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, IsOpen s → IsOpen t → IsOpen (s ∩ t)- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 98 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 15 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenstatement and proof · cited by 2,400
- TopologicalSpace.isOpen_interproof · cited by 1
Cited by99
Results whose statement or proof uses this declaration.
- isOpen_Iooproof · cited by 54
- nhds_basis_opensproof · cited by 54
- IsOpen.prodproof · cited by 22
- interior_interproof · cited by 22
- IsClosed.unionproof · cited by 17
- IsOpen.sdiffproof · cited by 8
- IsLocallyClosed.interproof · cited by 6
- Set.Finite.isOpen_sInterproof · cited by 6
- TopologicalSpace.le_generateFrom_iff_subset_isOpenproof · cited by 5
- uniformity_hasBasis_open_symmetricproof · cited by 4
- contMDiffAt_coordChangeLproof · cited by 3
- ContMDiffWithinAt.coordChangeproof · cited by 3