Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

For a ring R, Hilbert’s Tenth Problem HTP(R) is the set of polynomial equations over R, in several variables, with solutions in R. When R = Z, it is known that the jump Z′ is Turing-reducible to HTP(Z). We consider computability of HTP(R) for subrings R of the rationals. Applying measure theory to these subrings, which naturally form a measure space, relates their sets HTP(R) to the set HTP(Q),...

the purpose of the present study is to introduce the sequence space[{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},]where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. the topological properties and inclusion relations of this space are studied. moreover, the prob...

We prove that, up to topological conjugacy, every Smale space admits an Ahlfors regular Bowen measure. Bowen's construction of Markov partitions implies that spaces are factors chains. The latter equipped with Parry's measure which is regular. By extending we create a tool for transferring the regularity Parry down space. An essential part our method uses refined notion approximation graphs ove...

this paper is devoted to the concepts of fuzzy upper and fuzzy lower contra-continuous multifunctions and also some characterizations of them are considered.

Consider a set of continuous maps from the interval [0, 1] to a domain in R. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV functions) on the Wiener space and the theory of Dirichlet forms, we can discuss the existence of the surface measure and the Skorokhod representation of the reflecting Orn...

The Besicovitch and Weyl pseudometrics on the space AŸ of biinfinite sequences measure the density of differences in either the central or arbitrary segments of given sequences. The Besicovitch and Weyl spaces are obtained from A by factoring through the equivalence of zero distance. Cellular automata are considered as dynamical systems on the Besicovitch and Weyl spaces and their topological a...

As we have seen in the previous lecture, Teichmüller space T (S) for a surface of finite type S = Sg,n (genus g and n punctures or boundary components) is a parameter space for various types of structures that can be imposed on the same topological surface S. I’ll adopt the view that T (S) is the space of metrics on S, marked with a set of generators for the fundamental group, up to (measurable...

Andr es del Junco has proposed a deenition of topological minimal self-joinings intended to parallel Dan Rudolph's measure-theoretic concept. By means of a rank-two \cutting and stacking", this article constructs the rst example of a system (a subshift) satisfying his proposed deenition of 2-fold topological minimal self-joinings. The second part of the article shows that 2-fold topological min...