The images of absolute null sets (spaces) under bijective continuous mappings are studied. It is shown that, in general, these images do not possess regularity properties from the viewpoint of topological measure theory.
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References
M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities: Cauchy’s Equation and Jensen’s Inequality, PWN, Katowice (1985).
K. Kuratowski, Topology, Academic Press, London–New York (1966), Vol. 1.
A.W. Miller, “Special subsets of the real line,” in: Handbook of Set-Theoretic Topology, North-Holland, Amsterdam (1984).
J. C. Morgan II, Point Set Theory, Marcel Dekker, New York (1990).
J. C. Oxtoby, Measure and Category, Springer, New York (1971).
W. F. Pfeffer and K. Prikry, “Small spaces,” Proc. London Math. Soc., 58(3), No. 3, 417–438 (1989).
A. B. Kharazishvili, “Some properties of isodyne topological spaces,” Bull. Acad. Sci. Gruz. SSR, 127, No. 2, 261–264 (1987).
A. B. Kharazishvili, Nonmeasurable Sets and Functions, Elsevier, Amsterdam (2004).
P. Erd¨os, K. Kunen, and R. D. Mauldin, “Some additive properties of sets of real numbers,” Fund. Math., 113, No. 3, 187–199(1981).
A. B. Kharazishvili, “Sums of absolutely nonmeasurable functions,” Georg. Math. J., 20, No. 2, 271–282 (2013).
W. Sierpi’nski, “Sur la question de la mesurabilité de la base de M. Hamel,” Fund. Math., 1, 105–111 (1920).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 8, pp. 1134–1138, August, 2015.
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Kharazishvili, A. On Bijective Continuous Images of Absolute Null Sets. Ukr Math J 67, 1277–1282 (2016). https://doi.org/10.1007/s11253-016-1151-3
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DOI: https://doi.org/10.1007/s11253-016-1151-3