We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric structures. To represent both aspect of uncertainty, we choose an expected distance function as a measure of uncertainty. A formal logical system is constructed for the reasoning about expected distance. Soundness and completeness are shown f...

In this paper, some topological properties are discussed and results on completeness, totally boundedness, compactness parametric S-metric spaces developed.

Many palaeobiological analyses have concluded that modern birds (Neornithes) radiated no earlier than the Maastrichtian, whereas molecular clock studies have argued for a much earlier origination. Here, we assess the quality of the fossil record of Mesozoic avian species, using a recently proposed character completeness metric which calculates the percentage of phylogenetic characters that can ...

in this paper, we prove a common fixed point theorem for six mappings (two set valued and four single valued mappings) without assuming compatibility and continuity of any mapping on non complete metric spaces. to prove the theorem, we use a non compatible condition, that is, weak commutativity of type (kb). we show that completeness of the whole space is not necessary for the existence and uni...

We assume basic familiarity with the theory of metric spaces, in particular, the space of real numbers with its usual metric. In this section, we review some notation and a few basic definitions and theorems concerning metric spaces (including the concept of dimension zero). In §3 we use the completeness (or least upper bound) axiom of the real numbers in the form that says the space of real nu...

In this paper, we investigate a relationship between manyone-like autoreducibility and completeness for classes of functions computed by polynomial-time nondeterministic Turing transducers. We prove two results. One is that any many-one complete function for these classes is metric many-one autoreducible. The other is that any strict metric manyone complete function for these classes is strict ...

We show that quasi-metric or quasi-uniform spaces provide, inter alia, a common generalization of cpo's and metric spaces as used in denotational semantics. To accommodate the examples suggested by computer science, a reworking of basic notions involving limits and completeness is found to be necessary. Specific results include general fixed point theorem and a sequential completion construction.