Limits in Function Spaces and Compact Groups

Details Limits in Function Spaces and Compact Groups Limits in Function Spaces and Compact Groups

2003-02-19

arxiv.org/abs/math/0302239v1

Mathematics

General Topology

16 pages

Scientific paper

If B is an infinite subset of omega and X is a topological group, let C^X_B be the set of all x in X such that converges to 1. If F is a filter of infinite sets, let D^X_F be the union of all the C^X_B for B in F. The C^X_B and D^X_F are subgroups of X when X is abelian. In the circle group T, it is known that C^X_B always has measure 0. We show that there is a filter F such that D^T_F has measure 0 but is not contained in any C^X_B. There is another filter G such that D^X_G = T. We also describe the relationship between D^T_F and the D^X_F for arbitrary compact groups X.

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