Mathematica Bohemica, first online, pp. 1-7


On non-Baire rare sets in category bases

Sanjib Basu, Abhit Chandra Pramanik

Received March 19, 2024.   Published online March 3, 2025.

Abstract:  We deal with non-Baire rare sets in category bases which forms $\aleph_0$-independent family, where a rare set is a common generalization of both Luzin and Sierpinski set.
Keywords:  point-meager Baire base; countable chain condition; rare set; strictly $\aleph_0$-independent family; cofinality of cardinals; Ulam matrix
Classification MSC:  03E10, 03E50, 28A05, 54A05, 54E52

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References:
[1] M. Detlefsen, A. Szymański: Category bases. Int. J. Math. Math. Sci 16 (1993), 531-538. DOI 10.1155/S0161171293000651 | MR 1225498 | Zbl 0788.28001
[2] E. Hewitt, K. A. Ross: Abstract Harmonic Analysis. Vol. 1: Structure of Topological Groups. Integration Theory. Group Representations. Die Grundlehren der mathematischen Wissenschaften 115. Springer, Berlin (1963). DOI 10.1007/978-3-662-40409-6 | MR 0156915 | Zbl 0115.10603
[3] A. Kharazishvili: Nonmeasurable sets and functions. North-Holland Mathematics Studies 195. Elsevier, Amsterdam (2004). DOI 10.1016/s0304-0208(04)x8011-7 | MR 2067444 | Zbl 1082.28001
[4] A. Kharazishvili: Strange Functions in Real Analysis. CRC Press, Boca Raton (2018). DOI 10.1201/9781315154473 | MR 3645463 | Zbl 1375.26004
[5] K. Kuratowski, A. Mostowski: Set Theory: With an Introduction to Descriptive Set Theory. Studies in Logic and the Foundations of Mathematics 86. North-Holland, Amsterdam (1976). MR 0485384 | Zbl 0337.02034
[6] J. C. Morgan II: Infinite games and singular sets. Colloq. Math. 29 (1974), 7-17. DOI 10.4064/cm-29-1-7-17 | MR 0351821 | Zbl 0306.90103
[7] J. C. Morgan II: Baire category from an abstract viewpoint. Fundam. Math. 94 (1977), 13-23. DOI 10.4064/fm-94-1-59-64 | MR 0433416 | Zbl 0371.54014
[8] J. C. Morgan II: Point Set Theory. Pure and Applied Mathematics 131. Marcel Dekker, New York (1990). DOI 10.1201/9780203743010 | MR 1026014 | Zbl 0691.54001
[9] G. Pantsulaia: An application of independent families of sets to measure extension problem. Georgian Math. J. 11 (2004), 379-390. DOI 10.1515/GMJ.2004.379 | MR 2084996 | Zbl 1073.28008
[10] K. Schilling: Some category bases which are equivalent to topologies. Real Anal. Exchange 14 (1988/1989), 210-214. DOI 10.2307/44153639 | MR 0988366 | Zbl 0678.54021

Affiliations:   Sanjib Basu (corresponding author), Department of Mathematics, Bethune College, 181 Bidhan Sarani, Kolkata 700 006, West Bengal, India e-mail: sanjibbasu08@gmail.com; Abhit Chandra Pramanik, Department of Pure Mathematics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700019, West Bengal, India, e-mail: abhit.pramanik@gmail.com


 
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