Construction of a separately continuous function with given oscillation

  • 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
How to Cite
MaslyuchenkoV. K., and MaslyuchenkoO. V. “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.
Section
Research articles