2017
Том 69
№ 9

All Issues

Properties of the Ceder Product

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


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 $Y$.

English version (Springer): Ukrainian Mathematical Journal 67 (2015), no. 6, pp 881-890.

Citation Example: Maslyuchenko O. V., Maslyuchenko V. K., Myronyk O. D. Properties of the Ceder Product // Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 780-787.