Characterization of continuous functions by class C(infinity) curves

• Autorzy: Najdecki A. , Tabor J.
• Języki publikacji: EN

Abstrakty

EN

Let f : X -Y, where X is a Banach space and Y is a Hausdorff topological space. We prove that if f o (gamma) is continuous for every curve (gamma) : [0,1] -> X of class C(infinity), then f is continuous.

Słowa kluczowe

EN

curves; continuous functions; Banach space

PL

krzywe; funkcje ciągłe; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 31--34
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Najdecki A.

• Institute of Mathematics, University of Rzeszów, Rejtana 16A, 35-310 Rzeszów, Poland

autor

Tabor J.

• Institute of Mathematics, Jagiellonian University, Rejmonta 4, 30-059 Kraków, Poland

Bibliografia

• [RSS] W. Ring, P. Shöpf, J. Schwaiger, On functions continuous on certain classes of 'thin' sets, Publ. Math. Debrecen 51 no. 3-4 (1997), 205-224.
• [T1] J. Tabor, Note on metric spaces and continuous functions, Publ. Math. Debrecen 61 no. 1-2 (2002), 119-123.
• [T2] J. Tabor, Remark on the characterization of continuous function, Publ. Math. Debrecen 57 (2000), 307-313.