This paper continues the study of continuous selections begun in (13; 14; 15) and the
expository paper (12). The purpose of these papers, which is described in detail in the …

1. Introduction. The theory of selections, a systematic account of which appears in the
Annals of Mathematics [6][7][8], contains two theorems which are both of general interest …

Selections and Orderability Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAI
SOCIETY Volume 83, Number 3, November 1981 SELEC17IONS AND ORDERABILITY JAN …

1. Introduction. Let C be a convex subset of a linear topological space and E another linear
topological space. Suppose that T is a map from C to 2E, the family of all nonempty subsets …

-555 ls c, there is n0 e IN such that F (x0) c F (X)+(e/2) S. We have o (x)+ v** o F n0 e< o (x0),
thus there are ye F (x0) and rem, o (x)+ e< r* o (x0), such that S (y, r) c F (X 0). Therefore S (y …

Introduction.(The first two papers of this series are [3] and [4]. We continue here the notation
and terminology of [3].) Suppose L is a real linear system and let T be the collection of all …

Then-< a. But it follows from (ii) that il-? a. Therefore the sequence {Ki} has an empty
intersection and C is not weakly compact. Now suppose that C is bounded, closed, convex …

1. Introduction. The object of this paper is to establish certain properties of convex sets in a
setting as general as possible. This generality is perhaps interesting in itself since it …

A continuous selection theorem has been obtained for multivalued functions, the values of
which are convex sets of certain synthetic convex structures. Applications are given related …

The notion of convexity was generalized by many means. Some of these notions are useful
in questions of topology and analysis, for example, see [S, 12, 14-161. In this paper our aim …