6533b834fe1ef96bd129cb53

RESEARCH PRODUCT

Stoïlow’s theorem revisited

Pekka PankkaRami LuistoRami Luisto

subject

continuous open and discrete mappingsPure mathematicsContinuous open and light mappingscontinuous open and light mappingsFundamental theoremPicard–Lindelöf theoremGeneral Mathematics010102 general mathematicsRamsey theoryStoilow's theorem16. Peace & justice01 natural sciencesSqueeze theoremfunktioteoriaFactorizationStoilow’s theoremFundamental theorem of calculusContinuous open and discrete mappings111 Mathematics0101 mathematicsBrouwer fixed-point theoremMathematicsCarlson's theorem

description

Stoilow'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 -> 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. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed

yearjournalcountryeditionlanguage
2020-09-01Expositiones Mathematicae
https://doi.org/10.1016/j.exmath.2019.04.002