Theorems · Theorem · general topology
Filter.mem_map_iff_exists_image
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {m : α → β} {t : Set β}, t ∈ Filter.map m f ↔ ∃ s ∈ f, m '' s ⊆ t- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.preimageproof · cited by 4,946
- Filter.mapstatement and proof · cited by 819
- Filter.mem_of_supersetproof · cited by 308
- Set.image_preimage_subsetproof · cited by 75
- Filter.image_mem_mapproof · cited by 39
Cited by6
Results whose statement or proof uses this declaration.
- cauchySeq_tendsto_of_isCompleteproof · cited by 5
- UpperHalfPlane.isOpenMap_normproof · cited by 1
- Filter.mem_traverse_iffproof · cited by 1
- AbsoluteValue.IsEquiv.isEmbedding_equivWithAbsproof · cited by 1
- Filter.seq_assocproof · cited by 0
- Filter.prod_map_seq_commproof · cited by 0