The Bing plane and separately continuous mappings (in Ukrainian)

Author O. O. Karlova, V. K. Maslyuchenko, O. D. Myronyk
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Abstract We prove that the Bing plane $\mathbb{B}$ is $\sigma$-metrizable but not strongly $\sigma$-metrizable. Also we show that for $c$-connected topological spaces $X$ and $Y$ each separately continuous function $f:X\times Y\to \mathbb{B}$ is constant.
Keywords separately continuous function; the Bing plane; $\sigma$-metrizable spaces; continuum
Reference 1. Christensen J.P.R. Joint continuity of separately continuous functions// Proc. Amer. Math. Soc. 1981. V.82, 3. P. 455461.

2. Maslyuchenko V.K., Mykhaylyuk V.V., Filipchuk O.I. Points of joint continuity of separately continuous mappings with values in the Niemytski plane// Mat. Stud. 2006. V.26, 2. P. 217221. (in Ukrainian)

3. Maslyuchenko V.K., Mykhaylyuk V.V., Filipchuk O.I. Joint continuity of KhC-functions with values in Moore spaces// Ukr. Math. J. 2008. V.60, 11. P. 15391547. (in Ukrainian)

4. Maslyuchenko V.K., Filipchuk O.I. The essentiality of sigma-metrizability in results on joint continuity of KC-functions// Int. Conf. dedicated to the 125th anniversary of Hans Hahn. Book of Abstracts. Chernivtsi: Ruta, 2004. P. 6566. (in Ukrainian)

5. Maslyuchenko V.K., Myronyk O.D. Separately continuous mappings and stratifiable spaces// Mat. Visn. NTSH. 2010. V.7. P. 111121. (in Ukrainian)

6. Maslyuchenko V.K., Myronyk O.D. Joint continuity of mappings with values in various generalizations of metrizable spaces// Modern problems of Probability Theory and Mathematical Analysis. Book of Abstracts. Ivano-Frankivsk, 2012. P. 56. (in Ukrainian)

7. Bing R.H. A connected countable Hausdorff space. Proc. Amer. Math. Soc., V.4, 1953. 474 p.

8. Engelking R., General topology, revised and completed edition, Heldermann Verlag, Berlin, 1989.

9. Maslyuchenko V.K. Separately continuous mappings and Kothe spaces, Doctoral thesis. Chernivtsi, 1999. 345 p.

10. Filipchuk O.I. Separately continuous mappings and their analogs with values in non-metrizable spaces, PhD thesis. Chernivtsi, 2010. 124 p.

11. Karlova O.O., Myronyk O.D. Separately continuous mappings with values in the Bing plane// Int. Conf. Approximation Theory and its Applications dedicated to the 70th anniversary of O.I.Stepanets. Kyiv, 2012. P. 5152. (in Ukrainian)

Pages 188-193
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
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