Theorems · Definition · general topology
DiscreteQuotient.finsetClopens
(X : Type u_2) → [inst : TopologicalSpace X] → [CompactSpace X] → DiscreteQuotient X → Finset (TopologicalSpace.Clopens X)
If X is a compact space, then we associate to any discrete quotient on X a finite set of
clopen subsets of X, given by the fibers of proj.
TODO: prove that these form a partition of X
- Defined in
- Mathlib.Topology.DiscreteQuotient
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Finsetstatement · cited by 13,712
- Fintypeproof · cited by 7,736
- Set.preimageproof · cited by 4,946
- Set.rangeproof · cited by 4,705
- CompactSpacestatement and proof · cited by 593
- Fintype.ofFiniteproof · cited by 255
- Set.toFinsetproof · cited by 217
- DiscreteQuotientstatement and proof · cited by 65
- TopologicalSpace.Clopensstatement · cited by 53
- DiscreteQuotient.toSetoidproof · cited by 45
- DiscreteQuotient.projproof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- DiscreteQuotient.comp_finsetClopensstatement · cited by 1
- DiscreteQuotient.equivFinsetClopensstatement and proof · cited by 0
- DiscreteQuotient.finsetClopens.congr_simpstatement and proof · cited by 0
- DiscreteQuotient.finsetClopens_injstatement · cited by 0