Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777817 | Topology and its Applications | 2017 | 14 Pages |
Abstract
If Ï and Ï are two continuous real-valued functions defined on a compact topological space X and G is a subgroup of the group of all homeomorphisms of X onto itself, the natural pseudo-distance dG(Ï,Ï) is defined as the infimum of L(g)=âÏâÏâgââ, as g varies in G. In this paper, we make a first step towards extending the study of this concept to the case of Lie groups, by assuming X=G=S1. In particular, we study the set of the optimal homeomorphisms for dG, i.e. the elements Ïα of S1 such that L(Ïα) is equal to dG(Ï,Ï). As our main results, we give conditions that a homeomorphism has to meet in order to be optimal, and we prove that the set of the optimal homeomorphisms is finite under suitable conditions.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Alessandro De Gregorio,