Theorems · Theorem · general topology
IsDenseInducing.preconnectedSpace
∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {i : α → β}
[PreconnectedSpace α], IsDenseInducing i → PreconnectedSpace β- Defined in
- Mathlib.Topology.DenseEmbedding
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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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
- PreconnectedSpacestatement and proof · cited by 64
- IsDenseInducingstatement and proof · cited by 56
- IsDenseInducing.denseproof · cited by 20
- IsDenseInducing.continuousproof · cited by 4
- DenseRange.preconnectedSpaceproof · cited by 1
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