Characterization of segment and convexity preserving maps
Classical Analysis and ODEs
2012-12-07 v1
Abstract
In this note functions that transform open segments of a linear space into open segments of another linear space are studied and characterized. Assuming that the range is non-collinear, it is proved that such a map can always be expressed as the ratio of two affine functions.
Cite
@article{arxiv.1212.1268,
title = {Characterization of segment and convexity preserving maps},
author = {Zsolt Páles},
journal= {arXiv preprint arXiv:1212.1268},
year = {2012}
}