Cardinal Invariants Connected With Quotients Of Real Functions

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Abstract

We study cardinal invariants related to quotients in the case of the com- plement in ℝR of families of continuous, quasi-continuous, cliquish and Darboux functions.

Abstract

We study cardinal invariants related to quotients in the case of the com- plement in ℝR of families of continuous, quasi-continuous, cliquish and Darboux functions.

References

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  • 2. Ciesielski, K.; Maliszewski, A. - Cardinal invariants concerning bounded families of extendable and almost continuous functions, Proc. Amer. Math. Soc., 126 (1998), 471-479.

  • 3. Ciesielski, K.; Natkaniec, T. - Algebraic properties of the class of Sierpi´nski- Zygmund functions, Topology Appl., 79 (1997), 75-99.

  • 4. Grande, Z. - Sur la quasi-continuit´e et la quasi-continuit´e approximative, [Quasi- continuity and approximate quasicontinuity] Fund. Math., 129 (1988), 167-172.

  • 5. Grande, Z.; Natkaniec, T. - Lattices generated by T -quasicontinuous functions, Bull. Polish Acad. Sci. Math., 34 (1986), 525-530 (1987).

  • 6. Kempisty, S. - Sur les fonctions quasicontinues, Fund. Math., 19 (1932), 184-197.

  • 7. Jałocha, J. - Quotients of Darboux functions, Real Anal. Exchange, 26 (2000/01), 365-369.

  • 8. Jałocha, J. - Quotients of quasi-continuous functions, J. Appl. Anal., 6 (2000), 251-258.

  • 9. Jordan, F. - Cardinal invariants connected with adding real functions, Real Anal. Exchange, 22 (1996/97), 696-713.

  • 10. Kosman, J. - Cardinal invariants concerning closed graph functions, Demonstratio Math., 45 (2012), 813-819.

  • 11. Kosman, J. - Quotients of peripherally continuous functions, Cent. Eur. J. Math., 9 (2011), 765-771.

  • 12. Kosman, J.; Maliszewski, A. - Quotients of Darboux-like functions, Real Anal. Exchange, 35 (2010), 243-251.

  • 13. Natkaniec, T. - Almost continuity, Real Anal. Exchange, 17 (1991/92), 462-520.

  • 14. Neubrunnová, A. - On certain generalizations of the notion of continuity, Mat. ˇ C a s o p i s S l o v e n . A k a d . V i e d , 2 3 ( 1 9 7 3 ) , 3 7 4 -3 8 0 .

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1. Bartoszyński, T.; Judah, H. - Set theory. On the structure of the real line, A K Peters, Ltd., Wellesley, MA, 1995.

2. Ciesielski, K.; Maliszewski, A. - Cardinal invariants concerning bounded families of extendable and almost continuous functions, Proc. Amer. Math. Soc., 126 (1998), 471-479.

3. Ciesielski, K.; Natkaniec, T. - Algebraic properties of the class of Sierpi´nski- Zygmund functions, Topology Appl., 79 (1997), 75-99.

4. Grande, Z. - Sur la quasi-continuit´e et la quasi-continuit´e approximative, [Quasi- continuity and approximate quasicontinuity] Fund. Math., 129 (1988), 167-172.

5. Grande, Z.; Natkaniec, T. - Lattices generated by T -quasicontinuous functions, Bull. Polish Acad. Sci. Math., 34 (1986), 525-530 (1987).

6. Kempisty, S. - Sur les fonctions quasicontinues, Fund. Math., 19 (1932), 184-197.

7. Jałocha, J. - Quotients of Darboux functions, Real Anal. Exchange, 26 (2000/01), 365-369.

8. Jałocha, J. - Quotients of quasi-continuous functions, J. Appl. Anal., 6 (2000), 251-258.

9. Jordan, F. - Cardinal invariants connected with adding real functions, Real Anal. Exchange, 22 (1996/97), 696-713.

10. Kosman, J. - Cardinal invariants concerning closed graph functions, Demonstratio Math., 45 (2012), 813-819.

11. Kosman, J. - Quotients of peripherally continuous functions, Cent. Eur. J. Math., 9 (2011), 765-771.

12. Kosman, J.; Maliszewski, A. - Quotients of Darboux-like functions, Real Anal. Exchange, 35 (2010), 243-251.

13. Natkaniec, T. - Almost continuity, Real Anal. Exchange, 17 (1991/92), 462-520.

14. Neubrunnová, A. - On certain generalizations of the notion of continuity, Mat. ˇ C a s o p i s S l o v e n . A k a d . V i e d , 2 3 ( 1 9 7 3 ) , 3 7 4 -3 8 0 .

15. Rudin, M. - Martin’s Axiom, Handbook of Mathematical Logic, J. Barwise (ed.), North-Holland, Amsterdam-New York-Oxford (1977).

16. Thielman, H.P. - Types of functions, Amer. Math. Monthly, 60 (1953), 156-161.

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