σ-Continuous Functions and Related Cardinal Characteristics of the Continuum

[1] ADYAN, S. I.—NOVIKOV, P. S.: On a semicontinuous function, Moskov. Gos. Ped. Inst. Uč. Zap. 138 (1958), 3–10. (In Russian)Search in Google Scholar

[2] BANAKH, T.—MACHURA, M.—ZDOMSKYY, L.: On critical cardinalities related to Q-sets, Math. Bull. Shevchenko Sci. Soc. 11 (2014), 21–32.Search in Google Scholar

[3] BLASS, A.: Combinatorial cardinal characteristics of the continuum. In: Handbook of Set Theory, Vols. 1,2,3, Springer, Dordrecht, 2010, pp. 395–489.10.1007/978-1-4020-5764-9_7Search in Google Scholar

[4] CICHOŃ, J.—MORAYNE, M.—PAWLIKOWSKI, J.—SOLECKI, S.: Decomposing Baire functions, J. Symbolic Logic 56 (1991), 1273–1283.10.2307/2275474Search in Google Scholar

[5] DARJI, U.: Countable decomposition of derivatives and Baire 1 functions, J. Appl. Anal. 2 (1996), 119–124.10.1515/JAA.1996.119Search in Google Scholar

[6] GRZEGOREK, E.: Always of the first category sets. In: Proceedings of the 12th Winter School on Abstract Analysis (Srní 1984), Rend. Circ. Mat. Palermo (2) Suppl. No. 6, 1984, pp. 139–147.Search in Google Scholar

[7] GRZEGOREK, E.: Always of the first category sets. II. In: Proceedings of the 13th Winter Shool on Abstract Analysis (Srní 1985), Rend. Circ. Mat. Palermo (2) Suppl. No. 10, 1985, pp. 43–48.Search in Google Scholar

[8] GRZEGOREK, E.—RYLL-NARDZEWSKI, C.: On universal null sets, Proc. Amer. Math. Soc. 81 (1981), 613–617.10.1090/S0002-9939-1981-0601741-1Search in Google Scholar

[9] JACKSON, S.—MAULDIN, R.: Some complexity results in topology and analysis, Fund. Math. 141 (1992), 75–83.10.4064/fm-141-1-75-83Search in Google Scholar

[10] KECHRIS, A.: Classical Descriptive Set Theory, Graduate Texts in Mathematics Vol. 156, Springer-Verlag, New York, 1995.10.1007/978-1-4612-4190-4Search in Google Scholar

[11] KELDIŠ, L.: Sur les fonctions premières measurables B, Dokl. Akad. Nauk. SSSR 4 (1934), 192–197.Search in Google Scholar

[12] MILLER, A.: Special subsets of the real line. In: Handbook of Set-theoretic Topology. North-Holland, Amsterdam, 1984, pp. 201–233.10.1016/B978-0-444-86580-9.50008-2Search in Google Scholar

[13] PAWLIKOWSKI, J.—SABOK, M.: Decomposing Borel functions and structure at finite levels of the Baire hierarchy, Ann. Pure Appl. Logic 163 (2012), 1748–1764.10.1016/j.apal.2012.03.004Search in Google Scholar

[14] SIERPIŃSKI, W.: Sur un problème concernant les fonctions semi-continues, Fund. Math. 27 (1936), 191–200.10.4064/fm-27-1-191-200Search in Google Scholar

[15] SIERPIŃSKI, W.: Sur un problème concernant les fonctions de première classe, Fund. Math. 28 (1937), 1–6.10.4064/fm-28-1-1-6Search in Google Scholar

[16] SOLECKI, S.: Decomposing Borel sets and functions and the structure of Baire class 1 functions, J.Amer. Math.Soc. 11 (1998), 521–550.10.1090/S0894-0347-98-00269-0Search in Google Scholar

[17] STEPRĀNS, J.: A very discontinuous Borel function, J. Symbolic Logic 58 (1993), 1268–1283.10.2307/2275142Search in Google Scholar

[18] VAN DOUWEN, E. K.: The integers and topology. In: Handbook of Set-theoretic Topology, North-Holland, Amsterdam, 1984, pp. 111–167.10.1016/B978-0-444-86580-9.50006-9Search in Google Scholar

[19] VAN MILL, J.—POL, R.: Baire 1 functions which are not countable unions of continuous functions, Acta Math. Hungar. 66 (1995), 289–300.10.1007/BF01876046Search in Google Scholar

[20] VAUGHAN, J.: Small uncountable cardinals and topology. In: Open problems in topology, pp. 195–216. North-Holland, Amsterdam, 1990.Search in Google Scholar

[21] ZAPLETAL, J.: Descriptive set theory and definable forcing, Mem. Amer. Math. Soc. 167 (2004), viii+141.10.1090/memo/0793Search in Google Scholar