Theorems · Theorem · general topology
Filter.map_comap_of_surjective
∀ {α : Type u_1} {β : Type u_2} {f : α → β},
Function.Surjective f → ∀ (l : Filter β), Filter.map f (Filter.comap f l) = l- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.mapstatement · cited by 819
- Filter.comapstatement · cited by 546
- Function.Surjective.range_eqproof · cited by 70
- Filter.map_comap_of_memproof · cited by 9
Cited by11
Results whose statement or proof uses this declaration.
- OrderIso.map_atTopproof · cited by 11
- Filter.map_equiv_symmproof · cited by 4
- isProperMap_of_comp_of_surjproof · cited by 2
- Filter.comap_injectiveproof · cited by 2
- SeparationQuotient.map_mk_nhdsproof · cited by 2
- DilationEquiv.map_coboundedproof · cited by 2
- Function.Surjective.filter_map_topproof · cited by 1
- map_nhds_induced_of_surjectiveproof · cited by 0
- Homeomorph.map_coclosedCompactproof · cited by 0
- Homeomorph.map_cocompactproof · cited by 0
- SeparationQuotient.map_mk_nhdsSetproof · cited by 0