Generalized ultrametric spaces are a common generalization of preorders and ordinary ultrametric spaces (Lawvere 1973, Rutten 1995). Combining Lawvere's (1973) enriched-categorical and Smyth' (1987, 1991) topological view on generalized (ultra)metric spaces, it is shown how to construct 1. completion, 2. topology, and 3. powerdomains for generalized ultrametric spaces. Restricted to the special...

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets. Then we characterize the posets satisfying th...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere, 1973). Combining Lawvere’s (1973) enriched-categorical and Smyth’s (1988, 1991) topological view on generalized metric spaces, it is shown how to construct (1) completion, (2) two topologies, and (3) powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ...

a. csaszar introduced and extensively studied the notionof generalized open sets. following csazar, we introduce a new notionsuperconnected. the main purpose of this paper is to study generalizedsuperconnected spaces. various characterizations of generalized super-connected spaces and preservation theorems are discussed.

In the present article we continue recent work in the direction of domain theory were certain (accessible) categories are used as generalized domains. We discuss the possibility of using certain presheaf toposes as generalizations of the Scott topology at this level. We show that the toposes associated with Scott complete categories are injective with respect to dense inclusions of toposes. We ...

The following propositions are true: (1) Let X be a set and F be a finite family of subsets of X. Then there exists a finite family G of subsets of X such that G ⊆ F and ⋃ G = ⋃ F and for every subset g of X such that g ∈ G holds g 6⊆ ⋃ (G \ {g}). (2) Let S be a 1-sorted structure and X be a subset of the carrier of S. Then −X = the carrier of S if and only if X is empty. (3) Let R be an antisy...

Recently, Paiva et al. generalized the notion of overlap functions in context lattices and introduced a weaker definition, called quasi-overlap, that originates from removal continuity condition. In this paper, we introduce concept residuated implications related to quasi-overlap on prove some properties. We also show class fulfill residuation principle is same continuous according Scott topolo...

• The conditions are investigated under which the upper Vietoris topology coincides with Scott on K ( X ) . For a well-filtered space having first-countable Smyth power space, and coincide. T 0 in set of minimal elements any compact saturated subset, its is first-countable. Alexandroff double circle, first-countable, not , let be poset all non-empty sets reverse inclusion order. said to have pr...