Theorems · Definition · general topology
SeparatedNhds
{X : Type u_1} → [TopologicalSpace X] → Set X → Set X → PropSeparatedNhds is a predicate on pairs of subSets of a topological space. It holds if the two
subSets are contained in disjoint open sets.
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 60 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- IsOpenproof · cited by 2,400
- Disjointproof · cited by 2,201
Cited by35
Results whose statement or proof uses this declaration.
- SeparatedNhds.of_isCompact_isCompact_isClosedstatement · cited by 6
- SeparatedNhds.symmstatement and proof · cited by 6
- normal_separationstatement · cited by 5
- SeparatedNhds.disjoint_closure_leftstatement and proof · cited by 4
- Topology.IsClosedEmbedding.normalSpaceproof · cited by 2
- separatedNhds_iff_disjointstatement · cited by 2
- SeparatedNhds.disjoint_closure_rightstatement and proof · cited by 2
- SeparatedNhds.disjoint_nhdsSetstatement · cited by 2
- SeparatedNhds.isClosed_left_of_isClosed_unionstatement and proof · cited by 2
- SeparatedNhds.isOpen_left_of_isOpen_unionstatement and proof · cited by 2
- SeparatedNhds.monostatement and proof · cited by 2
- SeparatedNhds.of_finset_finsetstatement · cited by 2