Properties of the Ceder Product

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 Y . = Y \ b 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.