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