In this paper we investigate the role of domain representability and Scott-domain representability in the class of Moore spaces and the larger class of spaces with a base of countable order. We show, for example, that in a Moore space, the following are equivalent: domain representability; subcompactness; the existence of a winning strategy for player α (= the non-empty player) in the strong Ch...

This paper describes preference classes and preference Moore machines as a basis for integrating different hybrid neural representations. Preference classes are shown to provide a basic link between neural preferences and fuzzy representations at the preference class level. Preference Moore machines provide a link between recurrent neural networks and symbolic transducers at the preference Moor...

In this paper we investigate some properties of "autoepistemic logic" approach to the formalization of common sense reasoning suggested by R. Moore in [Moore, 19851. In particular we present a class of autoepistemic theories (called stratified autoepistemic theories) and prove that theories from this class have unique stable autoepistemic expansions and hence a clear notion of "theoremhood". Th...

The Moore bipartite bound represents an upper bound on the order of a bipartite graph of maximum degree ∆ and diameterD. Bipartite graphs of maximum degree ∆, diameterD and order equal to the Moore bipartite bound are called Moore bipartite graphs. Such bipartite graphs exist only if D = 2, 3, 4 and 6, and for D = 3, 4, 6, they have been constructed only for those values of ∆ such that ∆− 1 is ...

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

Property testing is a kind of randomized approximation in which one takes a small, random sample of a structure and wishes to determine whether the structure satisfies some property or is far from satisfying the property. We focus on the testability of classes of first-order expressible properties, and in particular, on the classification of prefixvocabulary classes for testability. The main re...

1. INTRODUCTION. The Moore Method is the best known—and arguably the most successful—way to train students to become creative research mathematicians. Here the term Moore Method (as capitalized) will refer only to the method as it was used by R. L. Moore—one of the towering figures of mathematics in America [65]— and not by his students or their descendants. Figure 1 shows the octogenarian Moor...

The first section of this paper is given over mainly to the investigation of linear Hausdorff spaces. However, the principal object of the paper is to characterize topologically that class of point sets used in the geometry for lines, namely, the class of simple continuous curves. This has already been done by R. L. Moore,f by R. L. Wilder, | and by myself.§ The results of this paper generalize...

In this paper, a class of Hessenberg matrices is presented for adoption as test matrices. The Moore-Penrose inverse and the Drazin inverse for each member of this class are determined explicitly.