Theorems · Definition · general topology
OnePoint.equivProjectivization
(K : Type u_1) → [inst : DivisionRing K] → [DecidableEq K] → OnePoint K ≃ Projectivization K (Fin 2 → K)
The one-point compactification of a division ring K is equivalent to
the projectivization ℙ K (Fin 2 → K).
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingDecidableEq
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.
- Equivstatement · cited by 8,337
- DivisionRingstatement and proof · cited by 1,062
- Matrix.vecConsproof · cited by 852
- Matrix.vecEmptyproof · cited by 832
- OnePointstatement and proof · cited by 126
- Projectivizationstatement and proof · cited by 111
- OnePoint.inftyproof · cited by 102
- OnePoint.someproof · cited by 76
- Projectivization.mkproof · cited by 55
- Projectivization.liftproof · cited by 3
- OnePoint.elimproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- OnePoint.smul_infty_eq_iteproof · cited by 4
- OnePoint.equivProjectivization_symm_apply_mkstatement · cited by 3
- OnePoint.smul_some_eq_iteproof · cited by 2
- OnePoint.smul_infty_defstatement and proof · cited by 1
- OnePoint.equivProjectivization_apply_coestatement · cited by 0
- OnePoint.equivProjectivization_apply_infinitystatement · cited by 0
- OnePoint.equivProjectivization_smulstatement and proof · cited by 0