Properties of the Ceder Product

  • V. K. Maslyuchenko
  • O. V. Maslyuchenko
  • O. D. Myronyk

Abstract

We study properties of the Ceder product $X ×_b Y$ of topological spaces $X$ and $Y$, where $b ∈ Y$, recently introduced by the authors. Important examples of the Ceder product are the Ceder plane and the Alexandroff double circle. In particular, for $i = 0, 1, 2, 3$ we establish necessary and sufficient conditions for the Ceder product to be a $T_i$ -space. We prove that the Ceder product $X ×_b Y$ is metrizable if and only if the spaces $X$ and $\overset{.}{Y}=Y\backslash \left\{b\right\}$ are metrizable, $X$ is $σ$-discrete, and the set $\{b\}$ is closed in $Y$. If $X$ is not discrete, then the point $b$ has a countable base of closed neighborhoods in $Y$.
Published
25.06.2015
How to Cite
MaslyuchenkoV. K., MaslyuchenkoO. V., and MyronykO. D. “Properties of the Ceder Product”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 6, June 2015, pp. 780-7, http://umj.imath.kiev.ua/index.php/umj/article/view/2021.
Section
Research articles