It is shown that any set-open topology on the automorphism group A(X) of a chain X coincides with the pointwise topology and that A(X) is a topological group with respect to this topology. Topological properties of connectedness and compactness in A(X) are investigated. In particular, it is shown that the automorphism group of a doubly homogeneous chain is generated by any neighborhood of the identity element.
@article{urn:eudml:doc:39188,
title = {Topological automorphism groups of chains.},
journal = {Mathware and Soft Computing},
volume = {8},
year = {2001},
pages = {47-60},
zbl = {0983.22004},
mrnumber = {MR1843689},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39188}
}
Ovchinnikov, Sergei V. Topological automorphism groups of chains.. Mathware and Soft Computing, Tome 8 (2001) pp. 47-60. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39188/