Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.isPreconnected_Icc
∀ {α : Type u_1} [inst : TopologicalSpace α] {K L : TopologicalSpace.NonemptyCompacts α},
IsPreconnected ↑L → IsPreconnected (Set.Icc K L)- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.Iccstatement and proof · cited by 1,702
- TopologicalSpace.Compactsproof · cited by 386
- IsPreconnectedstatement and proof · cited by 205
- Set.OrdConnectedproof · cited by 161
- TopologicalSpace.NonemptyCompactsstatement and proof · cited by 137
- Topology.IsEmbedding.toIsInducingproof · cited by 48
- TopologicalSpace.NonemptyCompacts.isEmbedding_toCompactsproof · cited by 12
- Topology.IsInducing.isPreconnected_imageproof · cited by 11
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