The additivity number of a topological property (relative to a given space) is the minimal number of subspaces with this property whose union does not have the property. The most well-known case is where this number is greater than א0, i.e. the property is σ-additive. We give a rather complete survey of the known results about the additivity numbers of a variety of topological covering properti...

A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y , separately continuous function f : X ×Y →R and open set I ⊆R, the set f −1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and c...

The basic concept of Type-2 Theory of Effectivity (TTE) to define computability on topological spaces ¢. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type-2 complexity theory on ...

Object substitution masking (OSM) is said to occur on an object level without a close spatiotemporal proximity of target and mask. An influential account for OSM is "object updating," which espouses that OSM occurs when the target is updated by the mask as they share a single object representation. However, it is unclear what attribute determines whether the mask shares the same object represen...

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...

Given an action of a finite group G on topological space, we can define its index. The G-index roughly measures size the given G-space. We explore connections between theory and dynamics. For fixed-point free dynamical system, study ℤp-index set p-periodic points. find that growth is at most linear in p. As application, construct system which does not have marker property. This solves problem h...

We study the topological models of a logic of knowledge for topological reasoning, introduced by Larry Moss and Rohit Parikh ([1992]). Among our results is a solution of a conjecture by the formentioned authors, finite satisfiability property and decidability for the theory of topological models.