Theorems · Theorem · general topology
Filter.subsingleton_iff_bot_or_pure
∀ {α : Type u_1} {l : Filter α}, l.Subsingleton ↔ l = ⊥ ∨ ∃ a, l = pure aA filter is a subsingleton iff it is equal to ⊥ or to pure a for some a.
- Defined in
- Mathlib.Order.Filter.Subsingleton
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Bot.botstatement and proof · cited by 4,720
- Filter.NeBotproof · cited by 853
- Filter.eq_or_neBotproof · cited by 62
- Filter.Subsingletonstatement and proof · cited by 15
- Filter.Subsingleton.exists_eq_pureproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Filter.Subsingleton.isCountablyGeneratedproof · cited by 0