Following the point-set lattice-theoretic (poslat) approach to topology of S. E. Rodabaugh [11], we introduced a more general way to do categorical (fuzzy) topology under the name of categorically-algebraic (catalg) topology [12], which unified many lattice-valued topological settings, and provided the means of intercommunication between different such frameworks. Moreover, motivated by the res...

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...

W is the category of archimedean l-groups with distinguished weak order unit, with l-group homomorphisms which preserve unit. This category includes all rings of continuous functions C(X) and all rings of measurable functions modulo null functions, with ring homomorphisms. The authors, and others, have studied previously the epimorphisms (right-cancellable morphisms) in W. There is a rich theor...

With the emergence of the fundamental paper [5] by Zadeh in 1965 number of papers have appeared in literature featuring the application of fuzzy sets to pattern recognition, decision problems, function approximation, system theory, fuzzy logic, fuzzy algorithms, fuzzy automata, fuzzy grammars, fuzzy languages, fuzzy algebras, fuzzy topology, etc. [2], [7]. In this note, our interests are in the...

A σ-frame is a poset with countable joins and finite meets in which binary meets distribute over countable joins. Aim of this paper is to present σ-frames, actually σ-locales, as a branch of Formal Topology, that is, intuitionistic and predicative pointfree topology. We show that every σframe L can be presented as the lattice of Lindelöf elements (those whose covers admit countable subcovers) o...

modeling and simulation of processing plants are widely used in industry. construction of a mathematical model for a plant is a time-consuming and error-prone task. in light of extensive advancements in computer science (both hardware and software), computers are becoming a necessary instrument in industrial activities. many software tools for modeling, simulation and optimization of processing...