Abstract
We study cardinal invariants connected with quotients in the case of functions that are constant, continuous, quasi-continuous, and cliquish on some interval or on no interval.
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T. Bartoszyński and H. Judah, Set Theory: On the Structure of the Real Line, A.K. Peters, Wellesley, MA, 1995.
K. Ciesielski, Set-theoretic real analysis, J. Appl. Anal., 3(2):143–190, 1997.
K. Ciesielski and T. Natkaniec, Algebraic properties of the class of Sierpiński–Zygmund functions, Topology Appl., 79(1):75–99, 1997.
K. Ciesielski and I. Recław, Cardinal invariants concerning extendable and peripherally continuous functions, Real Anal. Exch., 21(2):459–472, 1995–1996.
H. Fast, Une remarque sur la propriete de Weierstrass, Colloq. Math., 7:75–77, 1959.
Z. Grande, Sur la quasi-continuite et la quasi-continuite approximative, Fundam. Math., 129:167–172, 1988.
Z. Grande and T. Natkaniec, Lattices generated by T -quasi-continuous functions, Bull. Pol. Acad. Sci., Math., 34:525–530, 1986.
J. Jałocha, Quotients of quasi-continuous functions, J. App. Anal., 6(2):251–258, 2000.
F. Jordan, Cardinal invariants connected with adding real functions, Real Anal. Exch., 22(2):696–713, 1996–1997.
K.R. Kellum, Sums and limits of almost continuous functions, Colloq. Math., 31:125–128, 1974.
S. Kempisty, Sur les fonctions quasicontinues, Fundam. Math., 19:184–197, 1932.
J. Kosman, Quotients of peripherally continuous functions, Cent. Eur. J. Math., 9(4):765–771, 2011.
J. Kosman, Cardinal invariants concerning closed graph functions, Demonstr. Math., 45(4):813–819, 2012.
J. Kosman, Cardinal invariants connected with quotients of real functions, Annals of the Alexandru Ioan Cusa University – Mathematics, 2014 (forthcomming).
A. Lindenbaum, Sur quelques proprietes des fonctions de variable reelle, Ann. Soc. Math. Pol., 6:129–130, 1927.
T. Natkaniec, Almost continuity, Real Anal. Exch., 17(2):462–520, 1991–1992.
A. Neubrunnova, On certain generalizations of the notion of continuity, Mat. Čas., Slovensk. Akad. Vied, 23(4):374–380, 1973.
M.E. Rudin, Martin’s axiom, in J. Barwise (Ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 491–501.
H.P. Thielman, Types of functions, Am. Math. Monthly, 60(3):156–161, 1953.
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Kosman, J. Quotients of cliquish functions on some interval or on no interval. Lith Math J 54, 447–453 (2014). https://doi.org/10.1007/s10986-014-9255-7
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DOI: https://doi.org/10.1007/s10986-014-9255-7