Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777838 | Topology and its Applications | 2017 | 20 Pages |
Abstract
In the present paper we consider so-called saturated classes of frames of weight less than or equal to a given infinite cardinal Ï. Such classes are saturated by universal elements. We consider three kinds of saturated classes. The saturated classes of any considered kind have the following basic property: the intersection of not more than Ï many saturated classes is also a saturated class and therefore in this intersection there are also universal elements. We prove that the classes RegFrm(Ï) of regular and CRegFrm(Ï) of completely regular frames of weight â¤Ï are saturated classes in any of these kinds. This fact implies that in the classes RegFrm(Ï,μ) and CRegFrm(Ï,μ) of regular and completely regular frames, respectively, of weight â¤Ï and decomposition invariant (see [10]) μâ¤Ï there are universal elements.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
P.S. Gevorgyan, S.D. Iliadis, Yu.V. Sadovnichy,