Theorems · Theorem · general topology
ultrafilterBasis_is_basis
∀ {α : Type u}, TopologicalSpace.IsTopologicalBasis (ultrafilterBasis α)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Set.univproof · cited by 3,945
- Filter.mem_of_supersetproof · cited by 308
- Ultrafilterstatement and proof · cited by 193
- Filter.inter_memproof · cited by 153
- TopologicalSpace.IsTopologicalBasisstatement · cited by 126
- Filter.univ_memproof · cited by 96
- Set.eq_univ_of_forallproof · cited by 80
- Set.subset_sUnion_of_memproof · cited by 39
- Set.eq_univ_of_univ_subsetproof · cited by 7
- ultrafilterBasisstatement and proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- ultrafilter_isOpen_basicproof · cited by 5
- Ultrafilter.continuous_add_leftproof · cited by 2
- Ultrafilter.continuous_mul_leftproof · cited by 2