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
Maslyuchenko, V. K., O. V. Maslyuchenko, and O. D. Myronyk. “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