Theorems · Inductive type · general topology
Ultrafilter
Type u_2 → Type u_2
An ultrafilter is a minimal (maximal in the set order) proper filter.
- Defined in
- Mathlib.Order.Filter.Ultrafilter.Defs
- Cited by
- 193 results in Mathlib
- Foundations
- Depth 0 from the axioms, rests on 1 definitions · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by229
Results whose statement or proof uses this declaration.
- Ultrafilter.toFilterstatement and proof · cited by 172
- Filter.hyperfilterstatement · cited by 30
- IsCompact.prodproof · cited by 26
- Ultrafilter.mapstatement and proof · cited by 26
- Ultrafilter.ofstatement · cited by 15
- IsProperMap.isCompact_preimageproof · cited by 12
- Set.Finite.isCompact_biUnionproof · cited by 11
- Compactumproof · cited by 10
- Compactum.strstatement · cited by 9
- Ultrafilter.compl_mem_iff_notMemstatement and proof · cited by 9
- Ultrafilter.coe_injectivestatement and proof · cited by 8
- PreStoneCechproof · cited by 7
Showing the 200 most cited of 229.