In article some cardinal invariants of the space of finite subsets are examined. We obtained that such cardinal invariants us density and network weight, character and pi–character, pi–weight and weight coincide for any (A,B)–topology (Proposition 1). Also we obtained estimates of space of the finite subset of Lindelioft number and Suslin’s number (Theorem 2). Also is proved that for the space of finite subsets pseudo character is countable than and if than it’s diagonal number is countable for any (A,B)–topology (Proposition 4). Characterization when space of finite subsets has countable character is given (Proposition 5).