Gary Richardson

Predictive modeling techniques of software quality from software measures

The objective in the construction of models of software quality is to use measures that may be obtained relatively early in the software development life cycle to provide reasonable initial estimates of the quality of an evolving software system. Measures of software quality and software complexity to be used in this modeling process exhibit systematic departures of the normality assumptions of regression modeling. Two new estimation procedures are introduced, and their performances in the modeling of software quality from software complexity in terms of the predictive quality and the quality of fit are compared with those of the more traditional least squares and least absolute value estimation techniques. The two new estimation techniques did produce regression models with better quality of fit and predictive quality when applied to data obtained from two software development projects. >

Regular compactifications of convergence spaces

This note gives a simple characterization for the class of convergence spaces for which regular compactifications exist and shows that each such convergence space has a largest regular compactification. Introduction. It has been shown by Wyler [5] that for every Hausdorff convergence space S there is a regular (including Hausdorff) compact convergence space S* and a continuous map j: S-*S* with the following property: for every continuous map f: S-*T, where T is regular and compact, there is a unique continuous map g: S*--*T such that f=goj. Richardson [4] obtained a similar result, but with the following important distinctions: (1) the compactification space S* is Hausdorff but not necessarily regular (for convergence spaces, Hausdorff plus compact does not imply regular); (2) the mapj is a dense embedding. But there is in general no largest Hausdorff compactification, and indeed the number of distinct maximal Hausdorff compactifications can be quite large. The conclusions of both [4] and [5] suggest that a more satisfactory compactification theory for convergence spaces might result from an investigation of regular compactifications, although it is known (see [2]) that there are regular convergence spaces which cannot be embedded in any compact regular space. What we obtain in this note is a characterization of the class of convergence spaces for which regular compactifications exist, and we show that each such convergence space has a largest regular compactification. 1. For basic information about convergence spaces the reader is asked to refer to [1] and [2]. If there is no possibility of confusion, a convergence space (S, q) will be denoted simply by S. A space is regular if it is Hausdorff and has the property: F converges to x implies that the closure of Y (denoted cl ,) converges to x. We shall denote by cls A the closure of a subset A of a convergence space S. The pretopological modification rS of a convergence space (S, q) is the space (S, p), wherep is the finest pretopology Received by the editors March 3, 1971. AMS 1969 subject classifications. Primary 5410, 5453, 5423; Secondary 5422.

Completions of uniform convergence spaces

H. J. Biesterfeldt has shown that a uniform convergence space which satisfies the completion axiom has a completion. In the present paper, we show that every uniform convergence space has a completion. Furthermore, if the uniform convergence space is Hausdorff and satisfies the completion axiom, then it has a Hausdorff completion, which reduces to the Bourbaki completion for uniform spaces. Finally, a uniqueness theorem is obtained.

STRICT REGULAR COMPLETIONS OF CAUCHY SPACES

A diagonal condition is defined and used in characterizing the Cauchy spaces which have a strict, regular completion.