Convergence and quantale-enriched categories

Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category

Enriched lower separation axioms and the principle of enriched continuous extension

This paper presents a version of the lower separation axioms and the principle of enriched continuous extension for quantale-enriched topological spaces. As a remarkable result, among other things, we point out that in the case of commutative Girard quantales the principle of continuous extension holds for projective modules in Sup.<br/

Enriched lower separation axioms and the principle of enriched continuous extension

[EN] This paper presents a version of the lower separation axioms and the principle of enriched continuous extension for quantale-enriched topological spaces. As a remarkable result, among other things, we point out that in the case of commutative Girard quantales the principle of continuous extension holds for projective modules in Sup.The authors acknowledge support from the Basque Government (grant IT1483-22). The first named author also acknowledges support from a postdoctoral fellowship of the Basque Government (grant POS-2022-1-0015)

A Relation-Algebraic Approach to L - Fuzzy Topology

Any science deals with the study of certain models of the real world. However, a model is always an abstraction resulting in some uncertainty, which must be considered. The theory of fuzzy sets is one way of formalizing one of the types of uncertainty that occurs when modeling real objects. Fuzzy sets have been applied in various real-world problems such as control system engineering, image processing, and weather forecasting systems. This research focuses on applying the categorical framework of abstract L - fuzzy relations to L-fuzzy topology with ideas, concepts and methods of the theory of L-fuzzy sets. Since L-fuzzy sets were introduced to deal with the problem of approximate reasoning, t − norm based operations are essential in the definition of L - fuzzy topologies. We use the abstract theory of arrow categories with additional t − norm based connectives to define L - fuzzy topologies abstractly. In particular, this thesis will provide an abstract relational definition of an L - fuzzy topology, consider bases of topological spaces, continuous maps, and the first two separation axioms T0 and T1. The resulting theory of L - fuzzy topological spaces provides the foundation for applications and algorithms in areas such as digital topology, i.e., analyzing images using topological features

(bi)*-Neutrosophic Soft Limit Points in Neutrosophic Soft Bitopological Space

الهدف الرئيسي من البحث الحالي هو تقديم مفهوم "(bi) * - نقاط الحد اللينة المتعادلة" في فضاءات "نيوتروسوفتيك لينة بيتوبولوجية". بالإضافة إلى ذلك ، يهدف البحث إلى إعطاء النظريات الأساسية المتعلقة بالموضوع بأمثلة توضيحية.The major goal of the current research is to present the conception of “(bi)*-neutrosophic soft limit points” in “neutrosophic soft Bitopological” spaces. In addition, the research aims to give the essential theorems related to the topic with illustrative example