Let T be a topological space and let A be a subset of T . Recall that A is said to be a closed domain of T if A = IntA and A is said to be an open domain of T if A = IntA (see e.g. [8], [15]). Some simple generalization of these notions is the following one. A is said to be a domain of T provided IntA ⊆ A ⊆ IntA (see [15] and compare [7]). In this paper certain connections between these concept...

We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A positive consequence of the choice of morphisms is that those on the topological side are functional. Towards obtaining the topological duality, we develop a unive...

We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice Dirac and Laplace operators. Each of these techniques introduces ambiguities, which can invalidate the interpretation of the results. We show, however, that all ...

The lattice E of c.e. sets is a popular object of study in Computability Theory [So87]. A principal fact about this lattice is the undecidability of its first-order theory Th(E). Moreover, Th(E) is known [HN98] to be m-equivalent to the first-order arithmetic Th(N) where N := (ω; +,×). The lattice E may be considered as the lattice of effectively open subsets of the discrete topological space ω...

Let T be a topological space and let A be a subset of T . Recall that A is said to be a closed domain of T if A = IntA and A is said to be an open domain of T if A = IntA (see e.g. [8], [14]). Some simple generalization of these notions is the following one. A is said to be a domain of T provided IntA ⊆ A ⊆ IntA (see [14] and compare [7]). In this paper certain connections between these concept...

The relation between discrete topological field theories on triangulations of two-dimensional manifolds and associative algebras was worked out recently. The starting point for this development was the graphical interpretation of the associativity as flip of triangles. We show that there is a more general relation between flip-moves with two n-gons and Zn−2-graded associative algebras. A detail...

We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabili...

the fact that the properties of a molecule are tightly connected to its structural  characteristics  is one of the fundamental concepts in chemistry. in this connection,  graph theory has been successfully applied in developing some relationships between topological indices and some thermodynamic properties. so ,  a novel method for computing the new descriptors to construct a quantitative rela...

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 show that a particular twist of N = 4 super Yang-Mills in three dimensions with gauge group SU(2) possesses a set of classical vacua corresponding to the space of flat connections of the complexified gauge group SL(2, C). The theory also contains a set of topological observables corresponding to Wilson loops wrapping non-trivial cycles of the base manifold. This moduli space an...