The oscillation of quasi-continuous functions on pairwise attainable spaces

• Autores: Oleksandr V. Maslyuchenko
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 1, 2009, págs. 113-130
• Idioma: inglés
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• Resumen

  • We introduce a class of attainable and pairwise attainable spaces which includes metrizable spaces. On this classes we develop a new technique of constructing of functions with given oscillations. We characterize the oscillations of quasi-continuous functions. In particular, we prove that the function g defined on a pairwise attainable space is the oscillation of some quasi-continuous function f if and only if g is nonnegative upper semi-continuous function with a meager support.