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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.

Maximal classes for the family of quasi-continuous functions with closed graph

Sieg W.

Demonstratio Mathematica

2009

Vol. 42, nr 1

41-45

In this paper we consider classes of functions f : R - R. The maximal additive class for the family QU of quasi-continuous functions with closed graph is equal to the class of all continuous functions. We also show that the maximal multiplicative class for QU is equal to a class of continuous functions, which fulfil an extra condition.