We define a notion of morphism for quotient vector bundles that yields both a category QVBun and a contravariant global sections functor C : QVBun → Vect whose restriction to trivial vector bundles with fiber F coincides with the contravariant functor Top → Vect of F -valued continuous functions. Based on this we obtain a linear extension of the adjunction between the categories of topological ...

In recent years, models of spatial relations have attracted much attention from GIS community, especially topological relations. In this paper, some basic topologic models for spatial entities in both vector and raster spaces are discussed. To make the concepts more formalized, some new concepts from a new branch of mathematics -pansystems -are adopted. In doing so, the basic concepts of pansys...

1. Preliminaries, background and notation By ω, we shall denote the space of all real valued sequences. Any vector subspace of ω is called as a sequence space. We shall write l∞, c and c0 for the spaces of all bounded, convergent and null sequences, respectively. Also by bs, cs, l1 and lp, we denote the spaces of all bounded, convergent, absolutely and p-absolutely convergent series, respective...

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

A theorem of Luxemburg and Zaanen on normed Riesz spaces (Theorem 2.4 below) and one of Nakano (Theorem 2.3 below) have been extended by the author in [1] to metrizable locally solid linear topological Riesz spaces. This note gives an example which shows they cannot be further extended to nonmetrizable Hausdorff locally solid linear topological Riesz spaces. 1. Notation and basic concepts. For ...

This article is concerned with Alexandroff L-topological spaces and L-co-topological spaces, where L is a commutative, unital quantale. On one hand, an example is given to show that there is a finite strong L-topological space that is not Alexandroff. On the other hand, it is proved that every finite strong L-co-topological space is Alexandroff and that the category of Alexandroff strong L-co-t...