A1 Journal article (refereed)
Stoïlow's theorem revisited (2020)

Luisto, R., & Pankka, P. (2020). Stoïlow's theorem revisited. Expositiones Mathematicae, 38(3), 303-318. https://doi.org/10.1016/j.exmath.2019.04.002

JYU authors or editors

Luisto, Rami

Publication details

All authors or editors: Luisto, Rami; Pankka, Pekka

Journal or series: Expositiones Mathematicae

ISSN: 0723-0869

eISSN: 1878-0792

Publication year: 2020

Volume: 38

Issue number: 3

Pages range: 303-318

Publisher: Elsevier

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1016/j.exmath.2019.04.002

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/71752

Publication is parallel published: https://arxiv.org/abs/1701.05726

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→zk 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.

Keywords: complex analysis

Free keywords: continuous open and light mappings; continuous open and discrete mappings; Stoilow’s theorem

Fields of science: