Mathlib Map

Theorems · Theorem · general topology

Filter.map_bot

∀ {α : Type u_1} {β : Type u_2} {m : α → β}, Filter.map m ⊥ = ⊥
Defined in
Mathlib.Order.Filter.Map
Cited by
16 results in Mathlib
Foundations
Depth 62 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.

Filter.tendsto_bot · cited by 12Filter.tendsto_botFilter.map_eq_bot_iff · cited by 8Filter.map_eq_bot_iffFilter.limsup_bot · cited by 8Filter.limsup_botFilter.liminf_bot · cited by 4Filter.liminf_botessSup_measure_zero · cited by 2essSup_measure_zeromap_coe_atTop_of_Ioo_subset · cited by 2map_coe_atTop_of_Ioo_subs…HasFDerivWithinAt.empty · cited by 2HasFDerivWithinAt.emptyNNReal.toReal_limsup · cited by 1NNReal.toReal_limsuplimsup_const_sub · cited by 1limsup_const_subENNReal.toReal_essSup · cited by 1ENNReal.toReal_essSupENNReal.toReal_limsup · cited by 1ENNReal.toReal_limsupMeasureTheory.StronglyMeasurable.limUnder · cited by 1StronglyMeasurable.limUnd…Filter.vadd_filter_bot · cited by 0Filter.vadd_filter_botlimsup_sub_const · cited by 0limsup_sub_constIsUniformInducing.completableTopField · cited by 0IsUniformInducing.complet…Filter · cited by 8121FilterBot.bot · cited by 4720Bot.botFilter.map · cited by 819Filter.mapGaloisConnection.l_bot · cited by 63GaloisConnection.l_botFilter.gc_map_comap · cited by 12Filter.gc_map_comapFilter.map_botCITED BYCITES

Cites5

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

Cited by16

Results whose statement or proof uses this declaration.