Theorems · Theorem · general topology
PreconnectedSpace.isPreconnected_univ
∀ {α : Type u} {inst : TopologicalSpace α} [self : PreconnectedSpace α], IsPreconnected Set.univThe universal set Set.univ in a preconnected space is a preconnected set.
- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PreconnectedSpace
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.
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- IsPreconnectedstatement · cited by 205
- PreconnectedSpacestatement and proof · cited by 64
Cited by26
Results whose statement or proof uses this declaration.
- isConnected_univproof · cited by 9
- intermediate_value_univ₂proof · cited by 5
- isPreconnected_iff_preconnectedSpaceproof · cited by 4
- nonempty_interproof · cited by 2
- preconnectedSpace_iff_univproof · cited by 2
- hasFDerivAt_tsumproof · cited by 2
- connectedSpace_iff_univproof · cited by 2
- isPreconnected_rangeproof · cited by 2
- IsLocallyConstant.apply_eq_of_preconnectedSpaceproof · cited by 2
- subsingleton_of_preconnected_totallyDisconnectedproof · cited by 1
- AnalyticOnNhd.is_constant_or_isOpenMapproof · cited by 1
- hasDerivAt_tsumproof · cited by 1