Theorems · Theorem · general topology
connectedComponentIn_univ
∀ {α : Type u} [inst : TopologicalSpace α] (x : α), connectedComponentIn Set.univ x = connectedComponent x- Defined in
- Mathlib.Topology.Connected.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.univstatement · cited by 3,945
- Set.subset_univproof · cited by 228
- subset_antisymmproof · cited by 150
- connectedComponentstatement and proof · cited by 68
- connectedComponentInstatement · cited by 33
- mem_connectedComponentproof · cited by 21
- isPreconnected_connectedComponentproof · cited by 12
- IsPreconnected.subset_connectedComponentproof · cited by 10
- IsPreconnected.subset_connectedComponentInproof · cited by 6
- mem_connectedComponentInproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- isOpen_connectedComponentproof · cited by 3
- ampleSet_univproof · cited by 0
- Continuous.preimage_connectedComponentproof · cited by 0