In this paper we prove some results on the computational complexity of standard quantifierfree spatial logics with the connectedness predicate interpreted over the Euclidean spaces R and R. Topological logics with connectedness. A topological logic is a formal language whose variables range over subsets of topological spaces, and whose non-logical primitives denote fixed topological properties ...

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

Let E be an infinite-dimensional Hilbert space, and let H L(E) denote the Banach algebra of all functions f : D → L(E) that are holomorphic and bounded, equipped with the supremum norm ‖f‖∞ := supz∈D ‖f(z)‖L(E), f ∈ H ∞ L(E). We show that the Bass and topological stable ranks of H L(E) are infinite. If S is an open subset of T, then let A S L(E) denote the subalgebra of H L(E) of all functions ...

In the present paper we study some geometric objects and constructions related to groupoids of matrix subalgebras in a fixed matrix algebra. 1. The definition of groupoids In this paper we will freely use the notation from [3]. First recall some definitions and constructions [3]. 1.1. Groupoids Gk, l. Let Mkl(C) be the complex matrix algebra. Unital ∗-subalgebras isomorphic Mk(C) in some unital...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...

The aim of this paper is to study L-fuzzy uniformizable spaces. A new kind of topological fuzzy remote neighborhood system is defined and used for investigating the relationship between L-fuzzy co-topology and L-fuzzy (quasi-)uniformity. It is showed that this fuzzy remote neighborhood system is different from that in [23] when U is an Lfuzzy quasi-uniformity and they will be coincident when U ...

Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are ...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

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 large number of papers have been published that are devoted to showing that certain algebraic objects obtained by defining operations on the set of all continuous real-valued functions on a suitably restricted topological space determine the space. We mention but a few of them below. Let C(X), L(X), S(X) denote respectively the ring, lattice, multiplicative semigroup of all continuous real-va...