Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 393, Issue 1, Pages 138-143Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2012.03.007
Keywords
Algebrability; Perfectly everywhere surjective functions; Strongly everywhere surjective functions; Nowhere continuous Darboux functions; Nowhere continuous compact to compact functions
Categories
Funding
- Polish Ministry of Science and Higher Education [N N201 414939]
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We present the method of constructing algebras and linear spaces of 2' generators using independent Bernstein sets. As an application we obtain large algebras of special functions: (i) strongly everywhere surjective functions which are not perfectly everywhere surjective; (ii) nowhere continuous Darboux functions; (iii) nowhere continuous compact to compact functions; (iv) functions which are continuous precisely on a fixed closed proper subset of R. Most conclusions obtained in this paper-are improvements of some already known results. (C) 2012 Elsevier Inc. All rights reserved.
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