25,729 research outputs found
On constructions preserving the asymptotic topology of metric spaces
We prove that graph products constructed over infinite graphs with bounded
clique number preserve finite asymptotic dimension. We also study the extent to
which Dranishnikov's property C, and Dranishnikov and Zarichnyi's straight
finite decomposition complexity are preserved by constructions such as unions,
free products, and group extensions.Comment: 13 pages, accepted for publication in NC Journal of Mathematics and
Statistic
Countable Random Sets: Uniqueness in Law and Constructiveness
The first part of this article deals with theorems on uniqueness in law for
\sigma-finite and constructive countable random sets, which in contrast to the
usual assumptions may have points of accumulation. We discuss and compare two
approaches on uniqueness theorems: First, the study of generators for
\sigma-fields used in this context and, secondly, the analysis of hitting
functions. The last section of this paper deals with the notion of
constructiveness. We will prove a measurable selection theorem and a
decomposition theorem for constructive countable random sets, and study
constructive countable random sets with independent increments.Comment: Published in Journal of Theoretical Probability
(http://www.springerlink.com/content/0894-9840/). The final publication is
available at http://www.springerlink.co
Homology and closure properties of autostackable groups
Autostackability for finitely presented groups is a topological property of
the Cayley graph combined with formal language theoretic restrictions, that
implies solvability of the word problem. The class of autostackable groups is
known to include all asynchronously automatic groups with respect to a
prefix-closed normal form set, and all groups admitting finite complete
rewriting systems. Although groups in the latter two classes all satisfy the
homological finiteness condition , we show that the class of
autostackable groups includes a group that is not of type . We also show
that the class of autostackable groups is closed under graph products and
extensions.Comment: 20 page
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