Theorems · Theorem · general topology
Subtype.preconnectedSpace
∀ {α : Type u} [inst : TopologicalSpace α] {s : Set α}, IsPreconnected s → PreconnectedSpace ↑s- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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.Elemstatement · cited by 7,166
- Set.image_univproof · cited by 322
- IsPreconnectedstatement and proof · cited by 205
- PreconnectedSpacestatement · cited by 64
- Topology.IsInducing.subtypeValproof · cited by 43
- Subtype.range_valproof · cited by 41
- Topology.IsInducing.isPreconnected_imageproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- isPreconnected_iff_preconnectedSpaceproof · cited by 4
- Subtype.connectedSpaceproof · cited by 2
- IsPreconnected.induction₂'proof · cited by 1
- eq_of_germ_isConstant_onproof · cited by 0