Theorems · Theorem · general topology
DiscreteQuotient.isOpen_preimage
∀ {X : Type u_2} [inst : TopologicalSpace X] (S : DiscreteQuotient X) (A : Set (Quotient S.toSetoid)),
IsOpen (S.proj ⁻¹' A)- Defined in
- Mathlib.Topology.DiscreteQuotient
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimagestatement · cited by 4,946
- IsOpenstatement · cited by 2,400
- DiscreteQuotientstatement and proof · cited by 65
- DiscreteQuotient.toSetoidstatement and proof · cited by 45
- DiscreteQuotient.projstatement · cited by 23
- DiscreteQuotient.isClopen_preimageproof · cited by 3
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