Opuscula Mathematica
Opuscula Math. 35, no. 6 (), 973-978
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
Download this article's citation as:
a .bib file (BibTeX), a .ris file (RefMan), a .enw file (EndNote)
or export to RefWorks.

RSS Feed

horizontal rule

ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
Copyright © 2003−2017 OPUSCULA MATHEMATICA
Contact: opuscula@agh.edu.pl
Made by Tomasz Zabawa

horizontal rule

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.