We investigate what Ext(A, Z) can be when A is torsion-free and Hom(A, Z) = 0. We thereby give an answer to a question of Golasiński and Gonçalves which asks for the divisible Abelian groups which can be the type of a co-Moore space. 0. Introduction Marek Golasiński and Daciberg Lima Gonçalves have asked which divisible abelian groupsD can be the type of a co-Moore space [6, Problem 2.6]. In ot...

Models of spatial relations are a key component of geographical information science (GIS). EŒorts have been made to formally deŽ ne spatial relations. The foundationmodel for such a formal presentation is the 4-intersection model proposedby Egenhofer and Franzosa (1991). In this model, the topological relations between two simple spatial entities A and B are transformed into pointset topology p...

The fuzzy topological space was introduced by Dip in 1999 depending on the notion of spaces. Dip’s approach helps to rectify deviation some definitions subsets In this paper, further definitions, and theorems fill lack article. Different types are presented such as co-finite, co-countable, right left ray, usual topology. Furthermore, boundary, exterior, isolated points sets investigated illustr...

Currently, demands on 3D GIS increase, so spatial data analysis in 3D space also is required. Especially as large-scale and complex indoor space has been developed, it is more important to analyze human behaviors in complicated 3D indoor space to find accident spots or calculate evacuate routes. In order to do that, it is essential to represent topological relationships among the 3D entities in...

Network-based space layouts are fine-grained models of architectural spaces. They include rich spatial relationships between layout elements. Such information tends to be limited in existing space representations in building information modeling (BIM) systems. Network-based space layouts could be useful in the space planning and building automation domains. Their main feature is a geometric net...

Necessary and sufficient conditions are given so that the space C(X, E) of all continuous functions from a zero-dimensional topological space X to a nonArchimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly אo-barrelled, polarly `∞-barrelled or polarly co-barrelled. Also, tensor product...

Given an affine algebraic variety V and a quantization Oq(V ) of its coordinate ring, it is conjectured that the primitive ideal space of Oq(V ) can be expressed as a topological quotient of V . Evidence in favor of this conjecture is discussed, and positive solutions for several types of varieties (obtained in joint work with E. S. Letzter) are described. In particular, explicit topological qu...

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

In this note we provide a topological description of the MacNeille completion of a Heyting algebra similar to the description of the MacNeille completion of a Boolean algebra in terms of regular open sets of its Stone space. We also show that the only varieties of Heyting algebras that are closed under MacNeille completions are the trivial variety, the variety of all Boolean algebras, and the v...