Theorems · Theorem · general topology
Filter.comap_inf_principal_neBot_of_image_mem
∀ {α : Type u_1} {β : Type u_2} {f : Filter β} {m : α → β},
f.NeBot → ∀ {s : Set α}, m '' s ∈ f → (Filter.comap m f ⊓ Filter.principal s).NeBot- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Set.imagestatement and proof · cited by 5,609
- Filter.NeBotstatement and proof · cited by 853
- Filter.principalstatement · cited by 740
- Filter.comapstatement · cited by 546
- Filter.Eventually.frequentlyproof · cited by 44
- Filter.map_principalproof · cited by 17
- Filter.frequently_mem_iff_neBotproof · cited by 5
- Filter.neBot_inf_comap_iff_map'proof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- IsCompact.image_of_continuousOnproof · cited by 24
- Ultrafilter.comap_inf_principal_neBot_of_image_memproof · cited by 2
- IsLindelof.image_of_continuousOnproof · cited by 1
- IsCountablyCompact.imageproof · cited by 1