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Theorems · Theorem · general topology

Filter.ker_iSup

∀ {ι : Sort u_1} {α : Type u_2} (f : ι → Filter α), (⨆ i, f i).ker = ⋃ i, (f i).ker
Defined in
Mathlib.Order.Filter.Ker
Cited by
2 results in Mathlib
Foundations
Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

nhdsKer_iUnion · cited by 3nhdsKer_iUnionFilter.ker_sSup · cited by 1Filter.ker_sSupSet · cited by 53352SetFilter · cited by 8121FilterSet.iUnion · cited by 2483Set.iUnioniSup · cited by 2415iSupFilter.mem_of_superset · cited by 308Filter.mem_of_supersetsubset_antisymm · cited by 150subset_antisymmSet.subset_iUnion · cited by 81Set.subset_iUnionFilter.ker · cited by 40Filter.kerMonotone.le_map_iSup · cited by 8Monotone.le_map_iSupFilter.mem_iSup · cited by 3Filter.mem_iSupFilter.ker_mono · cited by 2Filter.ker_monoFilter.ker_iSupCITED BYCITES

Cites11

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Cited by2

Results whose statement or proof uses this declaration.