Theorems · Theorem · general topology
isOpen_nhdsKer
∀ {α : Type u_3} [inst : TopologicalSpace α] [AlexandrovDiscrete α] {s : Set α}, IsOpen (nhdsKer s)- Defined in
- Mathlib.Topology.AlexandrovDiscrete
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- IsOpenstatement and proof · cited by 2,400
- nhdsKerstatement · cited by 53
- AlexandrovDiscretestatement and proof · cited by 45
- isOpen_sInterproof · cited by 5
- nhdsKer_defproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- principal_nhdsKerproof · cited by 4
- nhdsKer_eq_iff_isOpenproof · cited by 1
- nhdsKer_subset_iffproof · cited by 1
- nhdsKer_mem_nhdsSetproof · cited by 0