Selecting families and their applications
Deguire and Lassonde [P. Deguire, M. Lassonde, Familles selectantes, Topol. Methods Nonlinear Anal. 5 (1995) 261-269] extend the concept of continuous selection and introduce the notion of selecting family for a family of set-valued mappings. In this paper, we first establish a new existence theorem of selecting families. The existence of the selecting families will be then used in order to obtain several fixed component theorems of Fan-Browder type, an intersection result, a maximal element theorem for a family of set-valued mappings and a minimax inequality.
A selection theorem and its applications
In this paper, we first prove an improved version of the selection theorem of Yannelis-Prabhakar and next prove a fixed point theorem in a non-compact product space. As applications, an intersection theorem and two equilibrium existence theorems for a non-compact abstract economy are given.
AXIOMATISABILITY OF WEAKLY FLAT, FLAT, AND PROJECTIVE S-ACTS
ABSTRACT This paper gives necessary and sufficient conditions on a monoid S that the class of flat left S-acts be (first order) axiomatisable. It presents also a streamlined version of the result of Stepanova that the class of projective left S-acts is axiomatisable if and only if the strongly flat left S-acts are axiomatisable and S is left perfect.