This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ⊳ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ⊳. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψL and the compacti...

Two generalized uniform structures namely fuzzy quasi-uniformity and fuzzy local quasi-uniformity are introduced. Conditions of fuzzy quasi-uniformizability and quasi-metrizability are examined. Mathematics Subject Classification: 54E15, 54A20

The purpose of this paper is to introduce Shi’s (quasi-)uniformity structure in the context of fuzzy soft sets. We define the notion of a fuzzy soft (quasi-)uniformity in the sense of Shi. We give the relations between a fuzzy soft (quasi-)uniformity and a fuzzy soft cotopology. Also, we investigate the relations between fuzzy soft remote neighborhood structures which are generated by a given f...

When testing that a sample of n points in the unit hypercube [0, 1] comes from a uniform distribution, the Kolmogorov–Smirnov and the Cramér–von Mises statistics are simple and well-known procedures. To encompass these measures of uniformity, Hickernell introduced the so-called generalized Lp-discrepancies. These discrepancies can be used in numerical integration through Monte Carlo and quasi–M...

We study conditions under which the Hausdorff quasi-uniformity UH of a quasi-uniform space (X,U) on the set P0(X) of the nonempty subsets of X is bicomplete. Indeed we present an explicit method to construct the bicompletion of the T0-quotient of the Hausdorff quasi-uniformity of a quasi-uniform space. It is used to find a characterization of those quasi-uniform T0spaces (X,U) for which the Hau...

Some new statistics are proposed to test the uniformity of random samples in the multidimensional unit cube [0, 1]d (d ≥ 2). These statistics are derived from number-theoretic or quasi-Monte Carlo methods for measuring the discrepancy of points in [0, 1]d. Under the null hypothesis that the samples are independent and identically distributed with a uniform distribution in [0, 1]d, we obtain som...

Abstract: Unlike a uniformity, a quasi-uniformity is not determined by its quasiuniform covers. However, a classical construction, due to Fletcher, which assigns a transitive quasi-uniformity to each family of interior-preserving open covers, allows to describe all transitive quasi-uniformities on the topological spaces in terms of those families of covers. In this paper we develop a pointfree ...