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Images of Bernstein sets via continuous functions

Images of Bernstein sets via continuous functions AbstractWe examine images of Bernstein sets via continuous mappings.Among other results, we prove that there exists a continuous function f:ℝ→ℝ{f\colon\mathbb{R}\to\mathbb{R}}that maps every Bernstein subset of ℝ{\mathbb{R}}onto the whole real line.This gives the positive answer to a question of Osipov. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Images of Bernstein sets via continuous functions

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References (7)

Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1572-9176
eISSN
1572-9176
DOI
10.1515/gmj-2019-2041
Publisher site
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Abstract

AbstractWe examine images of Bernstein sets via continuous mappings.Among other results, we prove that there exists a continuous function f:ℝ→ℝ{f\colon\mathbb{R}\to\mathbb{R}}that maps every Bernstein subset of ℝ{\mathbb{R}}onto the whole real line.This gives the positive answer to a question of Osipov.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Dec 1, 2019

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