Theorems · Theorem · general topology
Filter.mem_map
∀ {α : Type u_1} {β : Type u_2} {f : Filter α} {m : α → β} {t : Set β}, t ∈ Filter.map m f ↔ m ⁻¹' t ∈ f- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.preimagestatement · cited by 4,946
- Filter.mapstatement · cited by 819
Cited by63
Results whose statement or proof uses this declaration.
- IsCompact.prodproof · cited by 26
- Summable.tendsto_cofinite_zeroproof · cited by 16
- Multipliable.tendsto_cofinite_oneproof · cited by 6
- OpenPartialHomeomorph.extend_image_target_mem_nhdsproof · cited by 4
- Topology.IsOpenEmbedding.image_mem_nhdsproof · cited by 4
- tendsto_tsum_compl_atTop_zeroproof · cited by 3
- IsAddFoelner.tendsto_nhds_meanproof · cited by 3
- compact_open_separated_add_rightproof · cited by 3
- TendstoUniformlyOnFilter.tendsto_atproof · cited by 3
- IsFoelner.tendsto_nhds_meanproof · cited by 3
- isCompact_pi_infiniteproof · cited by 3
- cauchySeq_of_controlledproof · cited by 2