We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all finite subspaces sampled from these spaces converge. This topology is metrized following Gromov’s idea of embedding two metric spaces isometrically into a common...

recently, rahimi et al. [comp. appl. math. 2013, in press] dened the conceptof quadrupled xed point in k-metric spaces and proved several quadrupled xed pointtheorems for solid cones on k-metric spaces. in this paper some quadrupled xed point resultsfor t-contraction on k-metric spaces without normality condition are proved. obtainedresults extend and generalize well-known comparable result...

Generalizing the notion of a recursively enumerable (r.e.) set to sets of real numbers and other metric spaces is an important topic in computable analysis (which is the Turing machine based theory of computable real number functions). A closed subset of a computable metric space is called r.e. closed, if all open rational balls which intersect the set can be effectively enumerated and it is ca...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

In this paper, we prove a general fixed point theorem in $textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $textrm{S}$-metric spaces.

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

In this paper we show that a result of Gross and Kuelbs, used to study Gaussian measures on Banach spaces, makes it possible to construct an adjoint for operators on separable Banach spaces. This result is used to extend well known theorems of von Neumann and Lax. We also partially solve an open problem on the existence of a Markushevich basis with unit norm and prove that all closed densely de...

In programming language semantics different kinds of semantical domains are used, among them Scott domains and metric spaces. D. Scott raised the problem of finding a suitable class of spac~ which should include Scott domains and metric spaces such that effective mappings between these spaces are continuous. It is well known that between spaces like effectively given Scott domains or constructi...

3 Work done so far 4 3.1 Planning with Homotopy class constraints . . . . . . . . . . . . . . . . . . . . . . 4 3.1.1 The problem in 2 dimensions . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1.2 The problem in 3 dimensions . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.3 Generalization and extension to higher dimensions . . . . . . . . . . . . . 6 3.2 Metric information using ...

If X is a metric space then CX and LX denote the semigroups of continuous and Lipschitz mappings, respectively, from X to itself. The relative rank of CX modulo LX is the least cardinality of any set U \LX where U generates CX . For a large class of separable metric spaces X we prove that the relative rank of CX modulo LX is uncountable. When X is the Baire space NN, this rank is א1. A large pa...