Abstract We study a characterization of the precompactness sets in variable exponent Morrey spaces on bounded metric measure spaces. Totally are characterized from several points view for case over This is new constant exponents.

We have proven the absence of totally geodesic surfaces bounded or punctured by either the figure-eight knot or the 62 link. We’ve also found a case (Borromean Rings checkerboard) in which a Dehn filling changes a surface that is not totally geodesic into one that is.

Prompted by a recent question of G. Hjorth [12] as to whether a bounded Urysohn space is indivisible, that is to say has the property that any partition into finitely many pieces has one piece which contains an isometric copy of the space, we answer this question and more generally investigate partitions of countable metric spaces. We show that an indivisible metric space must be totally Cantor...

In this paper we study totally projective QTAG-modules and the extensions of bounded QTAG-modules. In the first section we study totally projective modules M/N and M ′/N ′ where N , N ′ are isomorphic nice submodules of M and M ′ respectively. In fact the height preserving isomorphism between nice submodules is extented to the isomorphism from M onto M ′ with the help of Ulm-Kaplansky invariant...

Let H be a Hilbert space, and A an inhabited, bounded, convex subset of B(H). We give a constructive proof that A is weak-operator totally bounded if and only if it is located relative to a certain family of seminorms that induces the strong-operator topology on B(H). 2000 Mathematics Subject Classification 03F60, 47S30 (primary)

We describe a conceptual approach which provides a unified view of various entropy-like functionals on the class of semimetric spaces, endowed with a bounded measure. The entropy E considered in the author’s previous articles is modified so as to assume finite values for a fairly wide class of spaces which fail to be totally bounded.

Let A be an infinite sign regular (sr) matrix which can be viewed as a bounded linear operator from lx to itself. It is proved here that if the range of A contains the sequence (...,1,-1,1,-1,...), then A is onto. If A'' exists, then DA~'D is also sr, where D is the diagonal matrix with diagonal entries alternately 1 and -1. In case A is totally positive (tp), then DA~]D is also tp under additi...

Abstract We extend the Polydisk Theorem for symmetric bounded domains to Cartan–Hartogs domains, and apply it prove that a domain inherits totally geodesic submanifolds from which is based on, give characterization of Cartan–Hartogs’s geodesics with linear support.

The present work introduces and justiies the notion of hy-perrobust learning where one xed learner has to learn all functions in a given class plus their images under primitive recursive operators. The following is shown: This notion of learnability does not change if the class of primitive recursive operators is replaced by a larger enumerable class of operators. A class is hyperrobustly Ex-le...