Results 1 
1 of
1
Locating Subsets Of A Hilbert Space
 Proceedings of the American Mathematical Society, 129(5):1385–1390, 2001. B.: Constructive Results on Operator Algebras
, 1998
"... . This paper deals with locatedness of convex subsets in inner product and Hilbert spaces which plays a crucial role in the constructive validity of many important theorems of analysis. 1. Introduction In Bishop's constructive mathematics, the framework of this paper, locatedness of subsets (especi ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
. This paper deals with locatedness of convex subsets in inner product and Hilbert spaces which plays a crucial role in the constructive validity of many important theorems of analysis. 1. Introduction In Bishop's constructive mathematics, the framework of this paper, locatedness of subsets (especially convex subsets) of normed spaces plays a crucial role in the validity of many important theorems of analysis such as the HahnBanach and separation theorems [1, Chapter 7.4], [7], the open and unopen mapping theorems [5], and the existence theorems of Minkowski functionals [9]. (Recall that subset C of a normed space X is located if (x; C) := inffkx yk : y 2 Cg exists for each x 2 X.) Richman [10] extended the denition of weakly totally boundedness, which was rst dened in [8] for separable Hilbert spaces, to inner product spaces which are not necessarily separable as follows: a subset C of an inner product space X is weakly totally bounded if for each x 2 X , fhx; yi : y 2 Cg i...