Theorems · Theorem · general topology
Topology.IsEmbedding.isTotallyDisconnected
∀ {α : Type u} {β : Type v} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set α},
Topology.IsEmbedding f → IsTotallyDisconnected (f '' s) → IsTotallyDisconnected s- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.imagestatement and proof · cited by 5,609
- Continuous.continuousOnproof · cited by 311
- Topology.IsEmbeddingstatement and proof · cited by 294
- Topology.IsEmbedding.injectiveproof · cited by 103
- Topology.IsEmbedding.continuousproof · cited by 51
- IsTotallyDisconnectedstatement and proof · cited by 14
- isTotallyDisconnected_of_imageproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.isTotallyDisconnected_imageproof · cited by 1