The discontinuity points set of separately continuous functions on the products of compacts
Abstract
It is solved a problem of construction of separately continuous functions on the product of compacts with a given discontinuity points set. We obtaine the following results. 1. For arbitrary \v{C}ech complete spaces , and a separable compact perfect projectively nowhere dense zero set there exists a separately continuous function the discontinuity points set of which equals to . 2. For arbitrary \v{C}ech complete spaces , and nowhere dense zero sets and there exists a separately continuous function such that the projections of the discontinuity points set of coincide with and respectively. An example of Eberlein compacts , and nowhere dense zero sets and such that the discontinuity points set of every separately continuous function does not coincide with , and -example of separable Valdivia compacts , and separable nowhere dense zero sets and such that the discontinuity points set of every separately continuous function does not coincide with are constructed.
Keywords
Cite
@article{arxiv.1512.07758,
title = {The discontinuity points set of separately continuous functions on the products of compacts},
author = {V. V Mykhaylyuk},
journal= {arXiv preprint arXiv:1512.07758},
year = {2015}
}