An algebraic criterion for local nondomination

The notion of a version locally noninferior by a binary relation is introduced that is an extension of the notion of local maximum to vectorial mappings. Differential conditions for local noninferiority are studied. For a class of smooth general functions of general position existence of an algebraical criterion of local noninf eriority of the verrsion is proved in the case of a binary relation specified by a field of semi-algebraical order cones.