Theorems · Theorem · general topology
Filter.mem_comap
∀ {α : Type u_1} {β : Type u_2} {g : Filter β} {m : α → β} {s : Set α}, s ∈ Filter.comap m g ↔ ∃ t ∈ g, m ⁻¹' t ⊆ s- Defined in
- Mathlib.Order.Filter.Map
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
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.comapstatement · cited by 546
Cited by13
Results whose statement or proof uses this declaration.
- nhds_inducedproof · cited by 32
- UniformSpace.mem_nhds_iffproof · cited by 7
- Filter.comap_embedding_atTopproof · cited by 4
- Filter.comap_embedding_atBotproof · cited by 3
- Dynamics.coverEntropy_image_of_comapproof · cited by 2
- Dynamics.coverEntropyInf_image_of_comapproof · cited by 2
- Valued.continuous_extensionproof · cited by 2
- LinearMap.isBigOTVS_rev_compproof · cited by 2
- Filter.comap_cofinite_leproof · cited by 1
- IsDenseInducing.extend_Z_bilinproof · cited by 1
- nhdsSet_inducedproof · cited by 1
- UniformSpace.ball_mem_nhdsWithinproof · cited by 1