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Theorems · Theorem · general topology

map_nhds_induced_eq

∀ {α : Type u_1} {β : Type u_2} [t : TopologicalSpace β] {f : α → β} (a : α),
  Filter.map f (nhds a) = nhdsWithin (f a) (Set.range f)
Defined in
Mathlib.Topology.Order
Cited by
1 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

Topology.IsInducing.map_nhds_eq · cited by 3IsInducing.map_nhds_eqTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsSet.range · cited by 4705Set.rangenhdsWithin · cited by 1912nhdsWithinFilter.map · cited by 819Filter.mapFilter.principal · cited by 740Filter.principalTopologicalSpace.induced · cited by 148TopologicalSpace.inducednhds_induced · cited by 32nhds_inducedFilter.map_comap · cited by 10Filter.map_comapmap_nhds_induced_eqCITED BYCITES

Cites10

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Cited by1

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