Theorems · Inductive type · general topology
TopologicalSpace.Clopens
(α : Type u_4) → [TopologicalSpace α] → Type u_4
The type of clopen sets of a topological space.
- Defined in
- Mathlib.Topology.Sets.Closeds
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
Cited by75
Results whose statement or proof uses this declaration.
- TopologicalSpace.Clopens.carrierstatement and proof · cited by 10
- PrimeSpectrum.isIdempotentElemEquivClopensstatement · cited by 10
- TopologicalSpace.Clopens.isClopen'statement and proof · cited by 5
- TopologicalSpace.Clopens.isClopenstatement and proof · cited by 3
- TopologicalSpace.Clopens.toOpensstatement and proof · cited by 3
- DiscreteQuotient.finsetClopensstatement · cited by 3
- ClopenUpperSet.toClopensstatement · cited by 2
- ContinuousMap.exists_finite_approximation_of_mem_nhds_diagonalproof · cited by 2
- TopologicalSpace.Clopens.mk.congr_simpstatement · cited by 2
- TopologicalSpace.Clopens.extstatement and proof · cited by 2
- TopologicalSpace.Clopens.isOpenstatement and proof · cited by 1
- TopologicalSpace.Clopens.toClosedsstatement and proof · cited by 1