Theorems · Theorem · general topology
nhdsSet_induced
∀ {α : Type u_5} {β : Type u_6} {t : TopologicalSpace β} (f : α → β) (s : Set α),
nhdsSet s = Filter.comap f (nhdsSet (f '' s))- Defined in
- Mathlib.Topology.NhdsWithin
- Cited by
- 1 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.
Cites11
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
- Filterstatement · cited by 8,121
- Set.imagestatement and proof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Filter.comapstatement and proof · cited by 546
- nhdsSetstatement and proof · cited by 267
- TopologicalSpace.inducedstatement · cited by 148
- Filter.extproof · cited by 60
- Filter.mem_comapproof · cited by 13
- mem_nhdsSet_inducedproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- map_nhdsSet_induced_eqproof · cited by 1