The natural lexicographic semigroupoids associated with Cantor product spaces indexed by countable linear orders are classified. Applications are given to the classification of triangular operator algebras which are direct limits of upper-triangular matrix algebras. 0. Introduction Consider a Cantor space which is presented explicitly as an infinite product of finite topological spaces. The pro...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

We adopt a novel topological approach for graphs, in which edges are modelled as points as opposed to arcs. The model of “classical” topologized graphs translates graph isomorphism into topological homeomorphism, so that all combinatorial concepts are expressible in purely topological language. This allows us to extrapolate concepts from finite graphs to infinite graphs equipped with a compatib...

We present a combinatorial description of those families 5a of sets, for which there is a finite measure p. such that inf{ß{P) : P 6 a"} > 0 . This result yields a topological characterization of measure-compactness and Borel measure-compactness. It is also applied to a problem on the existence of regular measure extensions. The main part of this paper deals with the following problem. Given a ...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

Topological extensions are closely related to nearness structures of various kinds. For example, the Smirnov compactification of a proximity space X is a compact Hausdorff space Y which contains X as a dense subspace and for which it is true that a pair of subsets of X is near if, and only if, their closures in Y meet. Lodato generalized this result to weaker conditions for the proximity and th...

A theorem on the existence of separable supports of σ-finite Borel measures given on metric spaces with small topological weights is applied to constructions of certain analogues of special subsets of the real line. A well-known result from topological measure theory states that every σ-finite Borel measure on a metric space whose weight is not real-valued measurable possesses a separable suppo...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

A scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented. The suggested scenario is along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and this author. To be able to apply the latter procedure to causal sets Sorkin’s ‘semantic switch’ from ‘partially ordered sets as finitary topological spaces’ to ...

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results repres...