Affine extensions of functions with a closed graph

• Autorzy: Wójtowicz M. , Sieg W.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.6.973

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

real-valued functions with a closed graph; points of discontinuity; affine extensions of functions

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 6
• Strony: 973--978
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Wójtowicz M.

• Uniwersytet Kazimierza Wielkiego Instytut Matematyki Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

autor

Sieg W.

• Uniwersytet Kazimierza Wielkiego Instytut Matematyki Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

Bibliografia

• [1] R.M. Aron, P.D. Berner, A Hahn-Banach extension theorem for analytic mappings, Bull. Soc. Math. France 106 (1978) 1, 3-24.
• [2] I. Baggs, Functions with a closed graph, Proc. Amer. Math. Soc. 43 (1974), 439-442.
• [3] J. Borsik, J. Dobos, M. Repicky, Sums of quasicontinuous functions with dosed graphs, Real Anal. Exch. 25 (1999/2000), 679-690.
• [4] K. Borsuk, liber Isomorphic der Funktionalraume, Bull. Int. Acad. Polon. Sci. (1933), 1-10.
• [5] S. Bromberg, An extension in class C1, Bol. Soc. Mat. Mex. II, Ser. 27 (1982), 35-44. [6] J. Dobos, Sums of closed graph functions, Tatra Mt. Math. Publ. 14 (1998), 9-11. [7] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math. 1 (1951), 353-367.
• [8] C.L. Fefferman, Cm extension by linear operators, Annals of Math. 166 (2007) 3, 779-835.
• [9] O.F.K. Kalenda, J. Spurny, Extending Baire-one functions on topological spaces, Topology Appl. 149 (2005) 1-3, 195-216.
• [10] K. Kuratowski, Sur les theoremes topologiques de la theorie des fonctions de variables reelles, C. R. Acad. Sci. Paris 197 (1933), 19-20.
• [11] J. Merrien, Prolongateurs de fonctions difjentiables d'une variable reelle, J. Math. Pures Appl. 45 (1966) 9, 291-309.
• [12] M. Wójtowicz, W. Sieg, P-spaces and an unconditional closed graph theorem, RACSAM 104 (2010) 1, 13-18.