Mikhail Suslin

Mikhail Y. Suslin
Born	(1894-11-15)15 November 1894 Krasavka, Saratov Oblast
Died	21 October 1919(1919-10-21) (aged 24) Krasavka, Saratov Oblast
Scientific career
Fields	General topology, descriptive set theory

Mikhail Yakovlevich Suslin (Russian: Михаи́л Я́ковлевич Су́слин; 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.

Biography

Mikhail Suslin was born on November 15, 1894, in the village of Krasavka, the only child of poor peasants Yakov Gavrilovich and Matrena Vasil'evna Suslin.^[1] From a young age, Suslin showed a keen interest in mathematics and was encouraged to continue his education by his primary school teacher, Vera Andreevna Teplogorskaya-Smirnova. From 1905 to 1913 he attended Balashov boys' grammar school.^[2]

In 1913, Suslin enrolled at the Imperial Moscow University and studied under the tutelage of Nikolai Luzin.^[1] He graduated with a degree in mathematics in 1917 and immediately began working at the Ivanovo-Voznesensk Polytechnic Institute.^[2]

Suslin died of typhus in the 1919 Moscow epidemic following the Russian Civil War, at the age of 24.

Work

His name is especially associated to Suslin's problem, a question relating to totally ordered sets that was eventually found to be independent of the standard system of set-theoretic axioms, ZFC.

He contributed greatly to the theory of analytic sets, sometimes called after him, a kind of a set of reals that 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 ${\displaystyle \mathbb {R} ^{2}}$, the projection onto the real axis was also a Borel set.

Publications

Suslin only published one paper during his life: a 4-page note.

• Souslin, M. Ya. (1917), "Sur une définition des ensembles mesurables B sans nombres transfinis", C. R. Acad. Sci. Paris, 164: 88–91
• Souslin, M. (1920), "Problème 3" (PDF), Fundamenta Mathematicae, 1: 223, doi:10.4064/fm-1-1-223-224
• Souslin, M. Ya. (1923), Kuratowski, C. (ed.), "Sur un corps dénombrable de nombres réels", Fundamenta Mathematicae (in French), 4: 311–315, doi:10.4064/fm-4-1-311-315, JFM 49.0147.03

See also

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 ⊆ 2^ω 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 and not order-isomorphic to the real line.

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.

References

1. O'Connor, John J.; Robertson, Edmund F. (March 2011). "Mikhail Yakovlevich Suslin". MacTutor History of Mathematics Archive. University of St Andrews.
2. Igoshin, V. I. (1996). "A short biography of Mikhail Yakovlevich Suslin". Russ. Math. Surv. 51 (3): 371–383. Bibcode:1996RuMaS..51..371I. doi:10.1070/RM1996v051n03ABEH002905. S2CID 250856671.

External links

• Mikhail Suslin at the Mathematics Genealogy Project