Opuscula Mathematica
Opuscula Math. 35, no. 6 (), 973-978
http://dx.doi.org/10.7494/OpMath.2015.35.6.973
Opuscula Mathematica

Affine extensions of functions with a closed graph



Abstract. Let \(A\) be a closed \(G_{\delta}\)-subset of a normal space \(X\). We prove that every function \(f_0: A\to\mathbb{R}\) with a closed graph can be extended to a function \(f: X\to\mathbb{R}\) with a closed graph, too. This is a consequence of a more general result which gives an affine and constructive method of obtaining such extensions.
Keywords: real-valued functions with a closed graph, points of discontinuity, affine extensions of functions.
Mathematics Subject Classification: 26A15, 54C20, 54D10.
Cite this article as:
Marek Wójtowicz, Waldemar Sieg, Affine extensions of functions with a closed graph, Opuscula Math. 35, no. 6 (2015), 973-978, http://dx.doi.org/10.7494/OpMath.2015.35.6.973
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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