Theorems · Theorem · general topology
ultrafilter_isClosed_basic
∀ {α : Type u} (s : Set α), IsClosed {u | s ∈ u}The basic open sets for the topology on ultrafilters are also closed.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- TopologicalSpaceproof · cited by 24,529
- Set.ofPredstatement and proof · cited by 6,101
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- Set.extproof · cited by 2,266
- IsClosedstatement · cited by 1,639
- Ultrafilterstatement and proof · cited by 193
- isOpen_compl_iffproof · cited by 63
- Ultrafilter.compl_mem_iff_notMemproof · cited by 9
- ultrafilter_isOpen_basicproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Hindman.exists_idempotent_ultrafilter_le_FPproof · cited by 1
- Hindman.exists_idempotent_ultrafilter_le_FSproof · cited by 1