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
< ω
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
The result of the Suslin operation is the set where the union is taken over all infinite sequences
is a family of subsets of a set
is the family of subsets of
obtained by applying the Suslin operation
to all collections as above where all the sets
The Suslin operation on collections of subsets of
is closed under taking countable unions or intersections, but is not in general closed under taking complements.
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
ω
ω
ω
be the infinite sequences that extend
This is a clopen subset of
ω
is a Polish space and
is a continuous function, let
is a Suslin scheme consisting of closed subsets of