𝔖 Bobbio Scriptorium
✦   LIBER   ✦

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

No coin nor oath required. For personal study only.

✦ 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


Addition Theorems for Finite Abelian Gro
✍ W.D. Gao 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 202 KB

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}

Limit theorems on locally compact Abelia
✍ Mátyás Barczy; Alexander Bendikov; Gyula Pap 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 221 KB 👁 1 views

## 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