Theorems · Definition · general topology
Compactum.str
(X : Compactum) → Ultrafilter X.A → X.A
The structure map for a compactum, essentially sending an ultrafilter to its limit.
- Defined in
- Mathlib.Topology.Category.Compactum
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Ultrafilterstatement · cited by 193
- CategoryTheory.Monad.Algebra.Astatement · cited by 81
- CategoryTheory.Monad.Algebra.aproof · cited by 45
- CategoryTheory.ofTypeMonadstatement · cited by 21
- Compactumstatement and proof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- Compactum.le_nhds_of_str_eqstatement and proof · cited by 2
- Compactum.str_eq_of_le_nhdsstatement and proof · cited by 2
- Compactum.isClosed_clproof · cited by 1
- Compactum.isClosed_iffstatement and proof · cited by 1
- Compactum.join_distribstatement and proof · cited by 1
- Compactum.str_hom_commutestatement and proof · cited by 1
- Compactum.str_inclstatement · cited by 1
- Compactum.lim_eq_strstatement and proof · cited by 0
- Compactum.cl_eq_closureproof · cited by 0