### On the action of the group of isometries on a locally compact metric space

Manoussos A (2010) .

Preprint | Englisch

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Einrichtung
Abstract / Bemerkung
In this short note we give an answer to the following question. Let $X$ be alocally compact metric space with group of isometries $G$. Let $\{g_i\}$ be anet in $G$ for which $g_ix$ converges to $y$, for some $x,y\in X$. What can wesay about the convergence of $\{g_i\}$? We show that there exist a subnet$\{g_j\}$ of $\{g_i\}$ and an isometry $f:C_x\to X$ such that $g_{j}$ convergesto $f$ pointwise on $C_x$ and $f(C_x)=C_{f(x)}$, where $C_x$ and $C_y$ denotethe pseudo-components of $x$ and $y$ respectively. Applying this we give shortproofs of the van Dantzig--van der Waerden theorem (1928) and Gao--Kechristheorem (2003).
Erscheinungsjahr
2010
Page URI
https://pub.uni-bielefeld.de/record/2298459

### Zitieren

Manoussos A. On the action of the group of isometries on a locally compact metric space. 2010.
Manoussos, A. (2010). On the action of the group of isometries on a locally compact metric space
Manoussos, A. (2010). On the action of the group of isometries on a locally compact metric space.
Manoussos, A., 2010. On the action of the group of isometries on a locally compact metric space.
A. Manoussos, “On the action of the group of isometries on a locally compact metric space”, 2010.
Manoussos, A.: On the action of the group of isometries on a locally compact metric space. (2010).
Manoussos, Antonios. “On the action of the group of isometries on a locally compact metric space”. (2010).

Open Data PUB

arXiv: 0902.0319