Theorems · Theorem · general topology
DiscreteQuotient.isClopen_setOfPred_rel
∀ {X : Type u_2} [inst : TopologicalSpace X] (S : DiscreteQuotient X) (x : X), IsClopen (Set.ofPred (S.toSetoid x))- Defined in
- Mathlib.Topology.DiscreteQuotient
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredstatement · cited by 6,101
- IsClopenstatement and proof · cited by 189
- DiscreteQuotientstatement and proof · cited by 65
- DiscreteQuotient.toSetoidstatement · cited by 45
- DiscreteQuotient.projproof · cited by 23
- DiscreteQuotient.isClopen_preimageproof · cited by 3
- DiscreteQuotient.fiber_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- DiscreteQuotient.isClopen_setOf_relproof · cited by 0