Theorems · Theorem · general topology
PreconnectedSpace.infinite
∀ {X : Type u_1} [inst : TopologicalSpace X] [PreconnectedSpace X] [Nontrivial X] [T1Space X], Infinite X- Defined in
- Mathlib.Topology.Separation.Connected
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Nontrivialstatement and proof · cited by 2,416
- Infinitestatement · cited by 352
- T1Spacestatement and proof · cited by 275
- PreconnectedSpacestatement and proof · cited by 64
- PreconnectedSpace.isPreconnected_univproof · cited by 26
- Set.nontrivial_univproof · cited by 4
- Set.infinite_univ_iffproof · cited by 3
- IsPreconnected.infinite_of_nontrivialproof · cited by 1
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