Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.preconnectedSpace_iff
∀ {α : Type u_1} [inst : TopologicalSpace α],
PreconnectedSpace (TopologicalSpace.NonemptyCompacts α) ↔ PreconnectedSpace α- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites14
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.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.univproof · cited by 3,945
- Set.singleton_subset_iffproof · cited by 206
- IsClopenproof · cited by 189
- TopologicalSpace.NonemptyCompactsstatement and proof · cited by 137
- PreconnectedSpacestatement and proof · cited by 64
- IsClopen.isOpenproof · cited by 21
- IsClopen.isClosedproof · cited by 12
- TopologicalSpace.NonemptyCompacts.isOpen_subsets_of_isOpenproof · cited by 4
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