For citation:
Старков В. В. A Countably Connected Domain is not Homeomorphic to an Uncountably Connected Domain. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 1, pp. 26-29. DOI: 10.18500/1816-9791-2013-13-1-1-26-29, EDN: SMXXGH
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
15.02.2013
Full text:
(downloads: 131)
Language:
Russian
Heading:
UDC:
517.53/54
EDN:
SMXXGH
A Countably Connected Domain is not Homeomorphic to an Uncountably Connected Domain
Autors:
Старков Виктор Васильевич, Petrozavodsk State University, Russia
Abstract:
In 1923 Керекьярто proved, that a countably connected domain is not homeomorphic to an uncountaby connected domain. We give another proof of this statement.
Key words:
References:
- Kerekjarto B. V. Vorlesungen über Topologie. Berlin : J. Springer, 1923. 270 p.
- Стоилов С. Лекции о топологических принципах теории аналитических функций. М. : Наука, 1964. 228 с. [Stoilov S. Lectures on topological principles in the theory of analytic functions. Moscow : Nauka, 1964. 228 p.]
- Старков В. В. Локально биголоморфные конечнолистные отображения ограниченных областей. // Сиб. мат. журн. 2011. Т. 52, № 1. С. 177–186. [Starkov V. V. Finitely valent locally biholomorphic mappings of bounded domains // Siberian Math. J. 2011. Vol. 52, № 1. P. 139–146.]
- Голузин Г. М. Геометрическая теория функций комплексного переменного. М. : Наука, 1966. 628 с. [Goluzin G. M. Geometric theory of Functions of a complex variable. Providence, R.I. : Amer. Math. Soc., 1969.]
- Александров П. С. Введение в теорию множеств и общую топологию. М. : Наука, 1977. 368 с. [Alexandrov P. C. Introduction to set theory and general topology. Moscow : Nauka, 1977. 368 p.]
Received:
20.08.2012
Accepted:
05.01.2013
Published:
15.02.2013
- 823 reads