Theorems · Theorem · general topology
ultrafilter_isOpen_basic
∀ {α : Type u} (s : Set α), IsOpen {u | s ∈ u}The basic open sets for the topology on ultrafilters are open.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 62 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.
- Setstatement and proof · cited by 53,352
- Set.ofPredstatement · cited by 6,101
- IsOpenstatement · cited by 2,400
- Ultrafilterstatement · cited by 193
- TopologicalSpace.IsTopologicalBasis.isOpenproof · cited by 31
- ultrafilterBasis_is_basisproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Ultrafilter.continuous_add_leftproof · cited by 2
- Ultrafilter.continuous_mul_leftproof · cited by 2
- ultrafilter_isClosed_basicproof · cited by 2
- induced_topology_pureproof · cited by 1
- isProperMap_iff_isClosedMap_ultrafilterproof · cited by 1