Theorems · Theorem · general topology
DenseRange.quotient
∀ {X : Type u} {Y : Type v} [inst : Setoid X] [inst_1 : TopologicalSpace X] {f : Y → X},
DenseRange f → DenseRange (Quotient.mk' ∘ f)The composition of Quotient.mk' and a function with dense range has dense range.
- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SetoidTopologicalSpace
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Cites6
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
- DenseRangestatement and proof · cited by 164
- Function.Surjective.denseRangeproof · cited by 21
- Quotient.mk''_surjectiveproof · cited by 19
- continuous_coinduced_rngproof · cited by 19
- DenseRange.compproof · cited by 9
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