Alexandroff and Scott Topologies for Generalized Metric Spaces

Alexandro and Scott Topologies for Generalized Metric Spaces

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces. Every generalized metric space can be isometrically embedded in a complete function space by means of a metric version of the categorical Yoneda embedding. This simple fact gives naturally rise to: 1. a topology for generalized metric spaces which for arbitrary preorders corresponds to the Alexandroo ...

Alexandroo and Scott Topologies for Generalized Ultrametric Spaces

Both preorders and ordinary ultrametric spaces are instances of generalized ul-trametric spaces. Every generalized ultrametric space can be isometrically embedded in a (complete) function space by means of an ultrametric version of the categorical Yoneda Lemma. This simple fact gives naturally rise to: 1. a topology for generalized ultrametric spaces which for arbitrary preorders corresponds to...

On Generalized Injective Spaces in Generalized Topologies

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...

Topologies for Probabilistic Metric Spaces

Scott Domains Generalized Ultrametric Spaces and Generalized Acyclic Logic Programs

Every Scott domain can be viewed as a generalized ultrametric space with proper ties which allow to apply a generalization of the Banach contraction mapping theorem We will give this construction in detail and apply it to a class of programs which is stricly larger than the class of all acyclic programs The paper is taken from Hit Chapter Domains as Generalized Ultrametric Spaces We rst introdu...