<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A classical theorem of W. Sierpiński, S. Mazurkiewicz and S. Kempisty says that the class of all differences of lower semicontinuous functions is uniformly dense in the space of all Baire-one functions. We show a generalization of this result to more general situations and derive an abstract theorem in the case of a binormal topological space.</p></abstract>

A classical theorem of W. Sierpiński, S. Mazurkiewicz and S. Kempisty says that the class of all differences of lower semicontinuous functions is uniformly dense in the space of all Baire-one functions. We show a generalization of this result to more general situations and derive an abstract theorem in the case of a binormal topological space.

Approximations by differences of lower semicontinuous functions

Department of Mathematics Pedagogical Faculty Catholic University Hrabovská cesta 1 SK-034-01 Ružomberok SLOVAKIA

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Approximations by differences of lower semicontinuous functions"}

A classical theorem of W. Sierpiński, S. Mazurkiewicz and S. Kempisty says that the class of all differences of lower semicontinuous functions is uniformly...

Approximations by differences of lower semicontinuous functions

Published Online: Sep 25, 2015

Page range: 183 - 190

Received: Jan 19, 2015

DOI: https://doi.org/10.1515/tmmp-2015-0015

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.