Stoïlow's theorem revisited
Abstract
Stoïlow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps $z\mapsto z^k$ and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.05726
 Bibcode:
 2017arXiv170105726L
 Keywords:

 Mathematics  Complex Variables;
 3002