The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first using quantities that have a direct correspondent in the case of a causal set, namely volumes, causal relations, and timelike lengths, as variables to describ...

In this paper, the Urysohn and completely Hausdorff axioms in general topology are generalized to L-topological spaces so as to be compatible with pointwise metrics. Some properties and characterizations are also derived

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...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

We prove a new quantitative version of the Alexandrov theorem which states that if mean curvature regular set in R^{n+1} is close to constant L^{n}-sense, then union disjoint balls with respect Hausdorff distance. This result more general than previous quantifications and using it we are able show R^2 R^3 weak solution volume preserving flow starting from finite perimeter asymptotically converg...

We take the well-known intuitionistic modal logic of Fischer Servi with semantics in bi-relational Kripke frames, and give the natural extension to topological Kripke frames. Fischer Servi’s two interaction conditions relating the intuitionistic pre-order (or partial-order) with the modal accessibility relation generalise to the requirement that the relation and its inverse be lower semi-contin...

In this note we prove a localized form of Alexandrov-Fenchel inequality for convex bodies, i.e. we prove a class of isoperimetric inequalities in a ball involving Federer curvature measures. 1991 Mathematics Subject Classification: 52A20, 52A39, 52A40, 49Q15.