In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

We deene the notion of weak relative pseudo-complement, and we show that, for an arbitrary lattice, the property of weak relative pseudo-complementation is strictly weaker than relative pseudo-complementation, but stronger than pseudo-complementation. Our main interest for this notion is in relation with the theory of closure operators. We prove that if a complete lattice L is completely inf-di...

Let dent A denote the set of denting points of a subset A of some Banach space. We prove dent cl co( K ® L) = dent K ® dent L for closed, bounded, absolutely convex subsets K and L of Banach spaces X and Y. Here the closure refers to the completion of X ® Y w.r.t. some reasonable crossnorm.

Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by ...

The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuo...

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind-MacNeille completion of P. The latticeK(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closu...

We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology. It is the weakest topology with respect to which the L-derivative operator, as a second order functional which maps the space of Lipschitz functions into the function space of non-empty weak* compact and convex valued maps equipped with the Scott topology, is continuo...