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...

Recently the Rydberg blockade effect has been utilized to realize quantum spin liquid on kagome lattice. Evidence of obtained experimentally by directly measuring non-local string order. In this letter, we report a BCS-type variational wave function study state in model. This is motivated mapping model lattice gauge theory, where local conservations replace role constraints from blockade. We de...

The aim of this paper is to introduce a further generalization of compactness in generalized topological spaces. We define and study the concept of Dμ-compact spaces in generalized topological spaces. A space(X, μ) is Dμ-compact if every Dμ-cover of X has a finite Dμ-sub cover. Basic properties and characterizations of Dμ-compact space are established. Dμ-compactness in subspaces, products of g...

A.Pushpalatha et al [11] introduced the concept of τ-g-closed set in topological spaces. S.Eswaran and A.Pushpalatha [6] introduced and studied the properties of τ-generalized continuous maps and τ-gc-irresolute maps in topological spaces. In this paper, we introduce and study a new class of maps called τ-generalized open maps and the notion of τ-generalized homeomorphism and τ-gchomeomorphism ...