On additive countably continuous functions

• Autores: T. Natkaniec
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 79, Fasc. 1-2, 2011, págs. 1-6
• Idioma: inglés
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• Resumen

  • We construct an example of additive Darboux function f : R --> R which is strongly countably continuous and discontinuous. We show also that if an additive function f is covered by countable family of continuous functions from R to R, then it can be also covered by countably many linear functions. Finally we remark that every finitely continuous and additive function is continuous.