Stationary subsets and stabilizers of restrictive Menger P-algebras of multiplace functions

Abstract

It is known [5], [6] that restrictive Menger algebras of multiplace functions are the sets of functions of fixed arity, which are stable for the operations of superposition, set-theoretical intersection and restrictive multiplication (i.e. the operation of the restriction of functions on domains of another functions). In the class of all such algebras we find the abstract characterization for sets of functions having some fixed point or the same fixed point for all functions of the given sets.