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

V. K. Maslyuchenko; O. V. Maslyuchenko; O. D. Myronyk

doi:10.15330/ms.43.1.78-87

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 $i\in\{1, 2, 2\frac 1 3, 2\frac 1 2, 3, 3\frac 1 2\}$).

1. Ceder J. Some generalizations of metric spaces, Pacif. J. Math., 11 (1961), 105–126.

2. Maslyuchenko V.K., Myronyk O.D. The Ceder product and stratifiable spaces, Buk. Math. J., 1 (2013), .1–2, 107–112. (in Ukrainian)

3. Engelking R. General Topology, M.: Mir, 1986, 752 p. (in Russian)

4. Caserta A., Watson S. The Alexandroff Duplicate and its subspaces, Applied General Topology, 8 (2007), №2, 187–205.

5. Buzyakova R.Z., Tkachuk V.V., Wilson R.G. A quest for nice kernels of neighbourhood assignments, Comment. Math. Univ. Carolin., 48 (2007), №4, 689–697.

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.

	On $L$-separatedness and $L$-regularity of the Ceder products
Author	V. K. Maslyuchenko, O. V. Maslyuchenko, O. D. Myronyk vmaslyuchenko@ukr.net, ovmasl@gmail.com, myronyk.oks@gmail.com 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	1. Ceder J. Some generalizations of metric spaces, Pacif. J. Math., 11 (1961), 105–126. 2. Maslyuchenko V.K., Myronyk O.D. The Ceder product and stratifiable spaces, Buk. Math. J., 1 (2013), .1–2, 107–112. (in Ukrainian) 3. Engelking R. General Topology, M.: Mir, 1986, 752 p. (in Russian) 4. Caserta A., Watson S. The Alexandroff Duplicate and its subspaces, Applied General Topology, 8 (2007), №2, 187–205. 5. Buzyakova R.Z., Tkachuk V.V., Wilson R.G. A quest for nice kernels of neighbourhood assignments, Comment. Math. Univ. Carolin., 48 (2007), №4, 689–697. 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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On $L$-separatedness and $L$-regularity of the Ceder products