Mikhail Yakovlevich Suslin
Mikhail Yakovlevich Suslin (Russian: Михаи́л Я́ковлевич Су́слин; Krasavka, Saratov Oblast, November 15, 1894 – 21 October 1919, Krasavka) (sometimes transliterated Souslin) was a Russian mathematician who made major contributions to the fields of general topology and descriptive set theory.
He contributed greatly to the theory of analytic sets, sometimes called after him, a kind of a set of reals which is definable via trees. In fact, while he was a research student of Nikolai Luzin (in 1917) he found an error in an argument of Lebesgue, who believed he had proved that for any Borel set in , the projection onto the real axis was also a Borel set.
Suslin only published one paper during his life: a 4-page note.
- Souslin, M. Ya. (1917), "Sur un définition des ensembles measurables B sans nombres transfinis", C.R. Acad. Sci. Paris, 164: 88–91
- Souslin, M. (1920), "Problème 3" (PDF), Fundamenta Mathematicae, 1: 223
- Souslin, M. Ya. (1923), Kuratowski, C., ed., "Sur un corps dénombrable de nombres réels", Fundamenta math. (in French), 4: 311–315, JFM 49.0147.03
- 1. A Suslin algebra is a Boolean algebra that is complete, atomless, countably distributive, and satisfies the countable chain condition
- 2. A Suslin cardinal is a cardinal λ such that there exists a set P ⊂ 2ω such that P is λ-Suslin but P is not λ'-Suslin for any λ' < λ.
- 3. The Suslin hypothesis says that Suslin lines do not exist
- 4. A Suslin line is a complete dense unbounded totally ordered set satisfying the countable chain condition
- 5. The Suslin number is the supremum of the cardinalities of families of disjoint open non-empty sets
- 6. The Suslin operation, usually denoted by A, is an operation that constructs a set from a Suslin scheme
- 7. The Suslin problem asks whether Suslin lines exist
- 8. The Suslin property states that there is no uncountable family of pairwise disjoint non-empty open subsets
- 9. A Suslin representation of a set of reals is a tree whose projection is that set of reals
- 10. A Suslin scheme is a function with domain the finite sequences of positive integers
- 11. A Suslin set is a set that is the image of a tree under a certain projection
- 12. A Suslin space is the image of a Polish space under a continuous mapping
- 13. A Suslin subset is a subset that is the image of a tree under a certain projection
- 14. The Suslin theorem about analytic sets states that a set that is analytic and coanalytic is Borel
- 15. A Suslin tree is a tree of height ω1 such that every branch and every antichain is at most countable.
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- Igoshin, V. I. (1996), "A short biography of Mikhail Yakovlevich Suslin", Russ. Math. Surv., 51 (3): 371–383, doi:10.1070/RM1996v051n03ABEH002905
- Akihiro Kanamori, Tenenbaum and Set theory (PDF), p. 2
- Mikhail Yakovlevich Suslin at the Mathematics Genealogy Project
- O'Connor, John J.; Robertson, Edmund F., "Mikhail Yakovlevich Suslin", MacTutor History of Mathematics archive, University of St Andrews.
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