Theorems · Theorem · general topology
DiscreteQuotient.isClopen_setOf_rel
Deprecated since 2026-07-09Use DiscreteQuotient.isClopen_setOfPred_rel instead.
∀ {X : Type u_2} [inst : TopologicalSpace X] (S : DiscreteQuotient X) (x : X), IsClopen (Set.ofPred (S.toSetoid x))Alias of DiscreteQuotient.isClopen_setOfPred_rel.
- Defined in
- Mathlib.Topology.DiscreteQuotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- Set.ofPredstatement · cited by 6,101
- IsClopenstatement · cited by 189
- DiscreteQuotientstatement · cited by 65
- DiscreteQuotient.toSetoidstatement · cited by 45
- DiscreteQuotient.isClopen_setOfPred_relproof · cited by 1
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