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Stoïlow’s theorem revisited
- Source :
- Expositiones Mathematicae. 38:303-318
- Publication Year :
- 2020
- Publisher :
- Elsevier BV, 2020.
-
Abstract
- 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.
- Subjects :
- continuous open and discrete mappings
Pure mathematics
Continuous, open and light mappings
continuous open and light mappings
Fundamental theorem
Picard–Lindelöf theorem
General Mathematics
010102 general mathematics
Ramsey theory
Stoilow's theorem
16. Peace & justice
01 natural sciences
Squeeze theorem
funktioteoria
Factorization
Stoilow’s theorem
Fundamental theorem of calculus
Continuous, open and discrete mappings
111 Mathematics
0101 mathematics
Brouwer fixed-point theorem
Mathematics
Carlson's theorem
Subjects
Details
- ISSN :
- 07230869
- Volume :
- 38
- Database :
- OpenAIRE
- Journal :
- Expositiones Mathematicae
- Accession number :
- edsair.doi.dedup.....05f24d3c2e3bad70781654ffc546f703