Theorems · Theorem · general topology
TopologicalSpace.Clopens.isOpen
∀ {α : Type u_2} [inst : TopologicalSpace α] (s : TopologicalSpace.Clopens α), IsOpen ↑s- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- SetLike.coestatement · cited by 8,199
- IsOpenstatement · cited by 2,400
- TopologicalSpace.Clopensstatement and proof · cited by 53
- IsClopen.isOpenproof · cited by 21
- TopologicalSpace.Clopens.isClopenproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- TopologicalSpace.Clopens.toOpensproof · cited by 3
- ContinuousMap.exists_finite_approximation_of_mem_nhds_diagonalproof · cited by 2