99 research outputs found
Ends of groups: a nonstandard perspective
We give a nonstandard treatment of the notion of ends of proper geodesic
metric spaces. We then apply this nonstandard treatment to Cayley graphs of
finitely generated groups and give nonstandard proofs of many of the
fundamental results concerning ends of groups. We end with an analogous
nonstandard treatment of the ends of relatively Cayley graphs, that is Cayley
graphs of cosets of finitely generated groups.Comment: 23 page
Nonstandard Hulls of Locally Exponential Lie Algebras
We show how to construct the nonstandard hull of certain infinite-dimensional
Lie algebras in order to generalize a theorem of Pestov on the enlargeability
of Banach-Lie algebras. In the process, we consider a nonstandard smoothness
condition on functions between locally convex spaces to ensure that the induced
function between the nonstandard hulls is smooth. We also discuss some
conditions on a function between locally convex spaces which guarantee that its
nonstandard extension maps finite points to finite points
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