摘要:

A semitopological quasigroup is defined and certain conditions are found under which a semitopological quasigroup is a topological quasigroup. Some properties of topological quasigroups are obtained. It is proved that (i) a realvalued continuous function defined on a compact subset of a topological left or right loop satisfying the second axiom of countability is uniformly continuous on it, (ii) a regular left or right Haar measure can be defined in any locally compact Hausdorff quasigroup satisfying certain conditions.

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631583

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The aim of this paper is to study the properties of component subcategories and related constructions. Component subcategories of the category of topological spaces have been defined by Herrlich and Strecker ([6]. [7], and [17]). In this paper a categorical definition is given which agrees with the topological definition.

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631584

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

In [7] the subject ofreproducing kernel Hilbert spaces(RKHSs) of linear functionals associated with linear operators and, in particular, with second-ordergeneralized stochastic processes(GSPs), is pursued. In this work these ideas are extended to nonlinear operators. As an example the characteristic operator of a GSP is pursued. The so-callednonlinear spaceof the process associated with the characteristic operator is investigated and the RKHS of functionals isometrically isomorphic to it is constructed. Unlike the linear space, the nonlinear analysis is not limited to second order GSPs.

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631585

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

A semi-quantitative theory of covering metric spaces is studied; the theory, involving the concept of a ‘fine cover’, has proved useful in complex analysis. We obtain general results on fine covers, and put forward some conjectures. Most of these remain unanswered (and indeed seem most difficult to answer) for subsets of the real line.

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631586

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

摘要:

The concept of a T-discrete object is a generalization of the notion of discrete spaces in concrete categories. In this paper. T-discrete objects are used to define discrete functors. Characterizations of discrete functors are given and their relation to other important functors are studied. A faithful functor T:A→Xis discrete iff the full subcategoryBofAconsisting of all T-discrete objects is (X-iso)-coreflective inA. It follows that the existence of bicoreflective subcategories is equivalent to the existence of suitable discrete functors. Finally, necessary and sufficient conditions are found such that for a given functor T:A→X, the full subcategoryBofAconsisting of all T-discreteA-objects is monocoreflective inA.

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631587

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631588

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1980.9631582

出版商:Taylor & Francis Group    

年代:1980

数据来源: Taylor