Metric and Topological Aspects of the Symmetric Group of Countable Degree

There is a natural topology on the symmetric group on an infinite set Ω . If Ω is countable , the topology is derived from a metric , and the group is complete . This paper gives an account of this topology , including translations of topological concepts for permutation groups , the use of Baire category and Haar measure , and some results about confinitary permutation groups which are motivated by the combinatorics of finite symmetric groups .