The classical Weil-Petersson metric on the Teichmüller space of compact Riemann surfaces is a Kähler metric, which is complete only in the case of elliptic curves [Wo]. It has a natural generalization to the deformation spaces of higher dimansional polarized Kähler-Einstein manifolds. It is still Kähler, and in the case of abelian varieties and K3 surfaces, the Weil-Petersson metric turns out t...

The aim of this paper to obtain completeness and uniqueness of fixed point theorem on b-metric space. In this paper we show that different contractive type mapping exist in b-metric space.

Metric spaces are generalized by many scholars. Recently, Khatami and Mirzavaziri use a mapping called t-definer to popularize the triangle inequality give generalization of notion metric, which is *-metric. In this paper, we prove that every *-metric space metrizable. Also, study total boundedness completeness spaces.

In the topological semantics for modal logic, S4 is well-known to be complete for the rational line, for the real line, and for Cantor space: these are special cases of S4’s completeness for any dense-in-itself metric space. The construction used to prove completeness can be slightly amended to show that S4 is not only complete, but also strongly complete, for the rational line. But no similarl...

In this paper, we give important properties as completeness, completion and precompactness of Hausdorff intuitionistic fuzzy metric spaces which is given by Gregori et al [13] and establish the precise relationship between the Hausdorff metric of a metric space (X, d) and the Hausdorff intuitionistic fuzzy metric of the standart intuitionistic fuzzy metric of d, and give two examples. AMS Subje...

This paper defines and discusses the Hausdorff metric on the space of nonempty, closed, and bounded subsets of a given metric space. We consider two important topological properties, completeness and total boundedness. We prove that each of these properties is posessed by a Hausdorff metric space if the property is possesed by the underlying metric space. Finally, we explore applications of the...

—Despite increasing concerns about the effect of sampling biases on our reading of the fossil record, few studies have considered the completeness of the fossil remains themselves, and those that have tend to apply non-quantitative measures of preservation quality. Here we outline two new types of metric for quantifying the completeness of the fossil remains of taxa through time, using sauropod...