On Alexandroff theorem for general Abelian groups
✍ Scribed by Alexander N. Dranishnikov; Dušan Repovš
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 111 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0166-8641
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✦ Synopsis
We present a technique for construction of infinite-dimensional compacta with given extensional dimension. We then apply this technique to construct some examples of compact metric spaces for which the equivalence Xτ M(G, n) ⇔ Xτ K(G, n) fails to be true for some torsion Abelian groups G and n 1.
📜 SIMILAR VOLUMES
Let \(a_{1}, \ldots, a_{k}\) be a sequence of elements in an Abelian group of order \(n\) (repetition allowed). In this paper, we give two sufficient conditions such that an element \(g \in G\) can be written in the form \(g=a_{i_{1}}+a_{i_{2}}+\cdots+a_{i_{n}}, 1 \leqslant i_{1}<i_{2}<\cdots<i_{n}
## Abstract We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem [4, Satz 1.3.6], since it does not have an easy access and it is not complete. This theorem giv