Theorems · Theorem · general topology
IsConnected.isPreconnected
∀ {α : Type u} [inst : TopologicalSpace α] {s : Set α}, IsConnected s → IsPreconnected s- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- IsPreconnectedstatement · cited by 205
- IsConnectedstatement and proof · cited by 116
Cited by36
Results whose statement or proof uses this declaration.
- IsConnected.imageproof · cited by 15
- Convex.isPreconnectedproof · cited by 14
- MeromorphicOn.exists_meromorphicOrderAt_ne_top_iff_forallproof · cited by 7
- Real.Angle.sign_eq_of_continuousOnproof · cited by 3
- MeasureTheory.exists_eq_setAverageproof · cited by 3
- isPreconnected_singletonproof · cited by 3
- Topology.IsCoinducing.isConnected_preimage_of_isClosedproof · cited by 3
- IsConnected.preimage_of_isOpenMapproof · cited by 2
- connectedComponentIn_mem_nhdsproof · cited by 2
- locallyConnectedSpace_iff_connected_subsetsproof · cited by 2
- Subtype.connectedSpaceproof · cited by 2
- AnalyticOn.hasFPowerSeriesOnSubballproof · cited by 2