Remarks on bounded sets in (LF )tv-spaces
نویسندگان
چکیده
We establish the relationship between regularity of a Hausdorff (LB)tv -space and its properties like (K), M.c.c., sequential completeness, local completeness. We give a sufficient and necessary condition for a Hausdorff (LB)tv-space to be an (LS)tv-space. A factorization theorem for (LN)tv-spaces with property (K) is also obtained.
منابع مشابه
FUZZY BOUNDED SETS AND TOTALLY FUZZY BOUNDED SETS IN I-TOPOLOGICAL VECTOR SPACES
In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.
متن کاملCharacterizations and properties of bounded $L$-fuzzy sets
In 1997, Fang proposed the concept of boundedness of $L$-fuzzy setsin $L$-topological vector spaces. Since then, this concept has beenwidely accepted and adopted in the literature. In this paper,several characterizations of bounded $L$-fuzzy sets in$L$-topological vector spaces are obtained and some properties ofbounded $L$-fuzzy sets are investigated.
متن کاملFunctionally 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 کاملCompleteness in Probabilistic Metric Spaces
The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...
متن کاملHomomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness
In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups including, n$-$Bourbaki-bounded homomorphisms and$hspace{1mm}$ B$-$Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous homomorphisms. So, two topologies are presented on them a...
متن کامل