On $L$-separatedness and $L$-regularity of the Ceder products

Author
V. K. Maslyuchenko, O. V. Maslyuchenko, O. D. Myronyk
Chernivtsi National University; Instytut Matematyki, Akademia Pomorska w Slupsku, Polska; Chernivtsi National University
Abstract
We study properties of the Ceder product $X \times_b Y$ of topological spaces $X$ and $Y$ with distinguished point $b\in Y$, recently introduced by the authors. Important examples of the Ceder product are the Ceder plane, the Alexandroff double circle and the Alexandroff duplicate. In particular, we detect Ceder products which are $L$-separated or $L$-regular (these notions generalize the separation axioms $T_i$ for $i\in\{1, 2, 2\frac 1 3, 2\frac 1 2, 3, 3\frac 1 2\}$).
Keywords
Separation axioms; linear separation axioms; the Ceder plane; Ceder product; Alexandroff double circle; Alexandroff duplicate; stratifiable space
DOI
doi:10.15330/ms.43.1.78-87
Reference
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2. Maslyuchenko V.K., Myronyk O.D. The Ceder product and stratifiable spaces, Buk. Math. J., 1 (2013), .1–2, 107–112. (in Ukrainian)

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6. Maslyuchenko V., Myronyk O. Stratifiability of the Ceder product, Vseukr. nauk. konf. ”Suchasni problemy teorii ymovirnostei ta matematychnogo analizu”. Tezy dopovidei, Iv.-Frankivs’k, 2012, 44– 45. (in Ukrainian)

7. Maslyuchenko V.K., Maslyuchenko O.V., Myronyk O.D. Properties of the Ceder product, Ukr. Mat. Zhurn. (to appear)

8. Banakh T., Ravsky A., Turek S., Kosztolovicz Z. Linear separation axioms, preprint.

Pages
78-87
Volume
43
Issue
1
Year
2015
Journal
Matematychni Studii
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