Theorems · Theorem · general topology
Filter.mem_of_eq_bot
∀ {α : Type u} {f : Filter α} {s : Set α}, f ⊓ Filter.principal sᶜ = ⊥ → s ∈ f- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bot.botstatement and proof · cited by 4,720
- Compl.complstatement and proof · cited by 2,925
- Filter.principalstatement and proof · cited by 740
- compl_complproof · cited by 229
- Filter.inf_principal_eq_botproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Ultrafilter.compl_notMem_iffproof · cited by 4
- IsLindelof.adherence_nhdsetproof · cited by 0
- IsCompact.adherence_nhdsetproof · cited by 0