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In mathematics, the **Suslin operation 𝓐** is an operation that constructs a set from a collection of sets indexed by finite sequences of positive integers.
The Suslin operation was introduced by Alexandrov (1916) and Suslin (1917). In Russia it is sometimes called the **A-operation** after Alexandrov. It is usually denoted by the symbol 𝓐 (a calligraphic capital letter A).

A **Suslin scheme** is a family of subsets of a set indexed by finite sequences of non-negative integers. The **Suslin operation** applied to this scheme produces the set

Alternatively, suppose we have a **Suslin scheme**, in other words a function from finite sequences of positive integers to sets . The result of the Suslin operation is the set

where the union is taken over all infinite sequences

If is a family of subsets of a set , then is the family of subsets of obtained by applying the Suslin operation to all collections as above where all the sets are in . The Suslin operation on collections of subsets of has the property that . The family is closed under taking countable unions or intersections, but is not in general closed under taking complements.

If is the family of closed subsets of a topological space, then the elements of are called **Suslin sets**, or analytic sets if the space is a Polish space.

For each finite sequence , let be the infinite sequences that extend . This is a clopen subset of . If is a Polish space and is a continuous function, let . Then is a Suslin scheme consisting of closed subsets of and .

- Aleksandrov, P. S. (1916), "Sur la puissance des ensembles measurables
*B*",*C. R. Acad. Sci. Paris*,**162**: 323–325 - "A-operation",
*Encyclopedia of Mathematics*, EMS Press, 2001 [1994] - Suslin, M. Ya. (1917), "Sur un définition des ensembles measurables
*B*sans nombres transfinis",*C. R. Acad. Sci. Paris*,**164**: 88–91