Mathlib Map

Theorems · Theorem · general topology

Filter.map_iSup

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_5} {m : α → β} {f : ι → Filter α},
  Filter.map m (⨆ i, f i) = ⨆ i, Filter.map m (f i)
Defined in
Mathlib.Order.Filter.Map
Cited by
4 results in Mathlib
Foundations
Depth 62 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.

AffineSpace.asymptoticNhds_vadd_pure · cited by 5AffineSpace.asymptoticNhd…IsCompact.prod_nhdsSet_eq_biSup · cited by 3IsCompact.prod_nhdsSet_eq…Filter.tendsto_iSup · cited by 2Filter.tendsto_iSupIsOpenMap.map_nhdsSet_eq · cited by 0IsOpenMap.map_nhdsSet_eqFilter · cited by 8121FilteriSup · cited by 2415iSupFilter.map · cited by 819Filter.mapGaloisConnection.l_iSup · cited by 78GaloisConnection.l_iSupFilter.gc_map_comap · cited by 12Filter.gc_map_comapFilter.map_iSupCITED BYCITES

Cites5

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

Cited by4

Results whose statement or proof uses this declaration.