Theorems · Theorem · general topology
DiscreteQuotient.eq_of_forall_proj_eq
∀ {X : Type u_2} [inst : TopologicalSpace X] [T2Space X] [CompactSpace X] [disc : TotallyDisconnectedSpace X] {x y : X},
(∀ (Q : DiscreteQuotient X), Q.proj x = Q.proj y) → x = y- Defined in
- Mathlib.Topology.DiscreteQuotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- T2Spacestatement and proof · cited by 1,351
- CompactSpacestatement and proof · cited by 593
- TotallyDisconnectedSpacestatement and proof · cited by 295
- IsClopenproof · cited by 189
- Set.mem_singleton_iffproof · cited by 172
- Set.mem_iInterproof · cited by 69
- DiscreteQuotientstatement and proof · cited by 65
- DiscreteQuotient.toSetoidstatement · cited by 45
- DiscreteQuotient.projstatement and proof · cited by 23
- Quotient.exact'proof · cited by 9
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