Metric and Topological Aspects of the Symmetric Group of Countable Degree

There is a natural topology on the symmetric group on an infinite setO.IfOis 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.