Inthispaper, (L,M)-fuzzy domain finiteness and (L,M)-fuzzy restricted hull spaces are introduced, and several characterizations of the category (L,M)-CS of (L,M)-fuzzy convex spaces are obtained. Then, (L,M)-fuzzy stratified (resp. weakly induced, induced) convex spaces are introduced. It is proved that both categories, the category (L,M)-SCS of (L,M)-fuzzy stratified convex spaces and the cate...

‎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  ...

1. When a system of sets covers a space, the star number of the covering is the supremum over the sets of the system of the cardinals of the numbers of sets of the system meeting a set of the system . The standard Lebesgue 'brick-laying' construction provides an example, for each positive integer n, of a lattice covering of R" by closed rectangular parallelepipeds with star number 2"T'-1 . In v...

By the relative distance of points p and q of a convex body C we mean the ratio of the Euclidean length of the segment pq to the half of the Euclidean length of a longest chord of C parallel to pq. We show that in the boundary of every plane convex body there exist seven points in pairwise relative distances at least 2 3 . We also give an estimate in case of three points. Finding sets of points...

Abstract In hyperbolic geometry there are several concepts to measure the breadth or width of a convex set. first part paper we collect them and compare their properties. Than introduce new concept thickness body. Correspondingly, define three classes bodies, bodies constant with, diameter having shadow property, respectively. We prove that property follows fulfilment both stronger as width. la...