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\(\mathbb Q\)-linear functions, functions with dense graph, and everywhere surjectivity. (English) Zbl 1159.46021

Summary: Let \(L\), \(S\) and \(D\) denote, respectively, the set of \(\mathbb Q\)-linear functions, the set of everywhere surjective functions and the set of dense-graph functions on \(\mathbb R\). In this note, we show that the sets \(D\setminus (S\cup L)\), \(S\setminus L\), \(S\cap L\) and \(D\cap L\setminus S\) are lineable. Moreover, all these sets contain (omitting zero) a vector space of the biggest possible dimension \(2^c\).

MSC:

46E99 Linear function spaces and their duals
26A99 Functions of one variable

Keywords:

lineability
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