Order Cancellation Law in a Semigroup of Closed Convex Sets

نویسندگان

چکیده

In this paper we generalize Robinson's version of an order cancellation law in which some unbounded subsets a vector space are cancellative elements. We introduce the notion weakly narrow sets normed spaces, study their properties and prove where canceled set is narrow. Also, for closed convex topological has bounded Hausdorff-like distance from its recession cone. topologically embed semigroup sharing cone having it into space. This result extends Bielawski Tabor's generalization Rådström theorem.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Functionally closed sets and functionally convex sets in real Banach spaces

‎Let $X$ be a real normed  space, then  $C(subseteq X)$  is  functionally  convex  (briefly, $F$-convex), if  $T(C)subseteq Bbb R $ is  convex for all bounded linear transformations $Tin B(X,R)$; and $K(subseteq X)$  is  functionally   closed (briefly, $F$-closed), if  $T(K)subseteq Bbb R $ is  closed  for all bounded linear transformations $Tin B(X,R)$. We improve the    Krein-Milman theorem  ...

متن کامل

functionally closed sets and functionally convex sets in real banach spaces

‎let $x$ be a real normed  space, then  $c(subseteq x)$  is  functionally  convex  (briefly, $f$-convex), if  $t(c)subseteq bbb r $ is  convex for all bounded linear transformations $tin b(x,r)$; and $k(subseteq x)$  is  functionally   closed (briefly, $f$-closed), if  $t(k)subseteq bbb r $ is  closed  for all bounded linear transformations $tin b(x,r)$. we improve the    krein-milman theorem  ...

متن کامل

Strong proximinality of closed convex sets

We show that in a Banach space X every closed convex subset is strongly proximinal if and only if the dual norm is strongly sub differentiable and for each norm one functional f in the dual space X∗, JX(f) the set of norm one elements in X where f attains its norm is compact. As a consequence, it is observed that if the dual norm is strongly sub differentiable then every closed convex subset of...

متن کامل

On Convergence of Closed Convex Sets

In this paper we introduce a convergence concept for closed convex subsets of a finite dimensional normed vector space. This convergence is called C-convergence. It is defined by appropriate notions of upper and lower limits. We compare this convergence with the well-known Painlevé–Kuratowski convergence and with scalar convergence. In fact, we show that a sequence (An)n∈N C-converges to A if a...

متن کامل

Finite Illumination of Unbounded Closed Convex Sets

If K is an unbounded closed convex subset of Ed having nonempty interior, we seek necessary and/or sufficient conditions to ensure that the boundary of K can be externally illuminated from a finite set of directions. This problem was stated as open in a recent book by Boltyanski. The tools used in this search are those developed by Visibility Theory such as the ideas of star, inner stem, visibi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Taiwanese Journal of Mathematics

سال: 2022

ISSN: ['1027-5487', '2224-6851']

DOI: https://doi.org/10.11650/tjm/220603