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.
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V. Maslyuchenko and O. Myronyk, “Stratifiability of the Ceder product,” in: Proc. Sci. Conf. “Contemporary problems of probability and mathematical analysis” (February, 20–26, 2012, Vorokhta, Ukraine), [in Ukrainian], Pre-Carpathian Univ., Ivano-Frankivsk (2012), pp. 44–45.
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V. K. Maslyuchenko and O. D. Myronyk, “Ceder product and stratifiable spaces,” Bukovinian. Math. J., 1, No. 1–2, 107–112 (2013).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 6, pp. 780–787, June, 2015.
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Maslyuchenko, V.K., Maslyuchenko, O.V. & Myronyk, O.D. Properties of the Ceder Product. Ukr Math J 67, 881–890 (2015). https://doi.org/10.1007/s11253-015-1120-2
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DOI: https://doi.org/10.1007/s11253-015-1120-2