On H1-compositors and piecewise continuous mappings (in Ukrainian)

Author O. O. Karlova, O. V. Sobchuk
Maslenizza.ua@gmail.com


Abstract We introduce the notion of a right $H_1$-compositor and prove that for a hereditarily Baire metrizable space $X$, a normal space $Y$ and a mapping $f\colon X\to Y$ the following conditions are equivalent: (i) $f$ is piecewise continuous; (ii) $f$ is $k$-continuous; (iii) $f$ is $G_\delta$-measurable; if, moreover, $Y$ is perfect, then (i)--(iii) are equivalent to: (iv) $f$ is a right $H_1$-compositor.
Keywords right $H_1$-compositor; right $B_1$-compositor; mapping of the first Lebesgue class; $G_\delta$-measurable mapping; piecewise continuous mapping; $k$-continuous mapping; weakly $k$-continuous mapping
Reference 1. Peng-Yee Lee, Wee-Kee Tang, Dongsheng Zhao, An equivalent definition of functions of the first Baire class, Proc. Amer. Math. Soc., 129 (2000), 8, 22732275.

2. J. Jachymski, M. Lindner, S. Lindner, On Cauchy type characterizations of continuity and Baire one functions, Real Anal. Exchange, 30 (2004/05), 1, 339346.

3. D. Lecomte, How we can recover Baire class one functions? Mathematika, 50 (2003), 1-2, 171198.

4. D.N. Sarkhel, Baire one functions, Bull. Inst. Math. Acad. Sinica, 31 (2003), 2, 143149.

5. D. Zhao, Functions whose composition with Baire class one functions are Baire class one, Soochow J. Math., 33 (2007), 4, 543551.

6. K. Kuratowski, Topology, V.1, New York, London, Warszawa, 1966.

7. R. Hansell, Borel measurable mappings for nonseparable metric spaces, Trans. Amer. Math. Soc., 161 (1971), 145168.

8. L. Vesel.y, Characterization of Baire-one functions between topological spaces, Acta Univ. Carol., Math. Phys., 33 (1992), 2, 143156.

9. O.O. Karlova, The decomposable and the ambiguous sets, Carpathian Math. Publications, 3 (2011), 2, 7176. (in Ukrainian)

10. T. Banakh, B. Bokalo, On scatteredly continuous maps between topological spaces, Topology Appl., 157 (2010), 1, 108122.

Pages 139-146
Volume 38
Issue 2
Year 2012
Journal Matematychni Studii
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