Mathlib Map

Theorems · Theorem · general topology

map_nhdsSet_induced_eq

∀ {α : Type u_5} {β : Type u_6} {t : TopologicalSpace β} {f : α → β} (s : Set α),
  Filter.map f (nhdsSet s) = nhdsSetWithin (f '' s) (Set.range f)
Defined in
Mathlib.Topology.NhdsWithin
Cited by
1 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Topology.IsInducing.map_nhdsSet_eq · cited by 1IsInducing.map_nhdsSet_eqSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121FilterSet.image · cited by 5609Set.imageSet.range · cited by 4705Set.rangeFilter.map · cited by 819Filter.mapFilter.principal · cited by 740Filter.principalnhdsSet · cited by 267nhdsSetTopologicalSpace.induced · cited by 148TopologicalSpace.inducednhdsSetWithin · cited by 25nhdsSetWithinFilter.map_comap · cited by 10Filter.map_comapnhdsSet_induced · cited by 1nhdsSet_inducedmap_nhdsSet_induced_eqCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.