Construction of a separately continuous function with given oscillation

Authors

  • V. K. Maslyuchenko
  • O. V. Maslyuchenko

Abstract

We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support can be covered by countably many sets, which are locally contained in products of sets of the first category.

Published

25.07.1998

Issue

Section

Research articles

How to Cite

Maslyuchenko, V. K., and O. V. Maslyuchenko. “Construction of a Separately Continuous Function With Given Oscillation”. Ukrains’kyi Matematychnyi Zhurnal, vol. 50, no. 7, July 1998, pp. 948–959, https://umj.imath.kiev.ua/index.php/umj/article/view/4875.