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Affine extensions of functions with a closed graph

Wójtowicz M., Sieg W.

Opuscula Mathematica

2015

Vol. 35, no. 6

973--978

Let A be a closed Gδ-subset of a normal space X. We prove that every function ƒ0 : A → R with a closed graph can be extended to a function ƒ: X → 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.