Theorems · Theorem · general topology
Filter.map_comap
∀ {α : Type u_1} {β : Type u_2} (f : Filter β) (m : α → β),
Filter.map m (Filter.comap m f) = f ⊓ Filter.principal (Set.range m)- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- le_antisymmproof · cited by 2,068
- Filter.mapstatement and proof · cited by 819
- Filter.principalstatement · cited by 740
- Filter.comapstatement and proof · cited by 546
- Filter.mem_of_supersetproof · cited by 308
- le_infproof · cited by 107
- Filter.le_principal_iffproof · cited by 87
- Filter.map_comap_leproof · cited by 10
Cited by10
Results whose statement or proof uses this declaration.
- Filter.map_comap_of_memproof · cited by 9
- Filter.map_comap_setCoe_valproof · cited by 2
- Filter.subtype_coe_map_comapproof · cited by 2
- isDiscrete_iff_nhdsWithinproof · cited by 2
- map_nhdsSet_induced_eqproof · cited by 1
- map_nhds_induced_eqproof · cited by 1
- map_uniformity_set_coeproof · cited by 1
- Complex.map_exp_comap_re_atBotproof · cited by 0
- Complex.map_exp_comap_re_atTopproof · cited by 0
- uniformEquicontinuous_restrict_iffproof · cited by 0