TY - JOUR
AU - V. K. Maslyuchenko
AU - O. V. Maslyuchenko
AU - O. D. Myronyk
PY - 2015/06/25
Y2 - 2023/03/28
TI - Properties of the Ceder Product
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 6
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2021
AB - 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 $Y$.
ER -