Opuscula Math. 35, no. 6 (2015), 973-978
http://dx.doi.org/10.7494/OpMath.2015.35.6.973

 
Opuscula Mathematica

Affine extensions of functions with a closed graph

Marek Wójtowicz
Waldemar Sieg

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.

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  • Marek Wójtowicz
  • Uniwersytet Kazimierza Wielkiego, Instytut Matematyki, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
  • Waldemar Sieg
  • Uniwersytet Kazimierza Wielkiego, Instytut Matematyki, Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland
  • Received: 2014-10-16.
  • Accepted: 2014-12-10.
Opuscula Mathematica - cover

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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