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Theorems · Theorem · general topology

map_snd_nhds

∀ {X : Type u} {Y : Type v} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] (x : X × Y),
  Filter.map Prod.snd (nhds x) = nhds x.2
Defined in
Mathlib.Topology.Constructions.SumProd
Cited by
1 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

isOpenMap_snd · cited by 3isOpenMap_sndTopologicalSpace · cited by 24529TopologicalSpaceFilter · cited by 8121Filternhds · cited by 5554nhdsSet.preimage · cited by 4946Set.preimagele_antisymm · cited by 2068le_antisymmnhdsWithin · cited by 1912nhdsWithinFilter.map · cited by 819Filter.mapinf_le_left · cited by 286inf_le_leftEq.trans_le · cited by 155Eq.trans_leFilter.map_mono · cited by 63Filter.map_monocontinuousAt_snd · cited by 12continuousAt_sndmap_snd_nhdsWithin · cited by 2map_snd_nhdsWithinmap_snd_nhdsCITED BYCITES

Cites12

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Cited by1

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