Maximums of internally quasi-continuous functions

Marciniak, Mariola; Szczuka, Paulina

doi:10.2478/v10127-012-0029-5

.blurhash-client-img { display: none !important; }

Maximums of internally quasi-continuous functions

Tatra Mountains Mathematical Publications

Volume 52 (2012): Issue 1 (August 2012)

By: Mariola Marciniak and Paulina Szczuka

Open Access

|Nov 2012

Abstract

In this paper, we characterize maximums of internally quasi-continuous functions, Darboux internally quasi-continuous functions, internally strong ´Swi¸atkowski functions, and lattices generated by these families of functions. Moreover, we examine maximal classes with respect to maximums for internally quasi- -continuous functions and Darboux internally quasi-continuous functions.

References

[1] BORS´IK, J.: Maxima and minima of simply continuous and quasicontinuous functions, Math. Slovaca 46 (1996), 261-268.
Search in Google Scholar
[2] FARKOV´A, J.: About the naximum and the minimum of Darboux functions, Mat. ˇCas. 21 (1971), 110-116.
Search in Google Scholar
[3] GRANDE, Z.-NATKANIEC, T.: Lattices generated by T -quasi-continuous functions, Bull. Polish Acad. Sci. Math. 34 (1986), 525-530.
Search in Google Scholar
[4] GRANDE, Z.-SOŁTYSIK, L.: Some remarks on quasi-continuous real functions, Problemy Mat. 10 (1988), 79-87.
Search in Google Scholar
[5] KEMPISTY, S.: Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184-197.10.4064/fm-19-1-184-197
Search in Google Scholar
[6] MALISZEWSKI, A.: On the limits of strong ´Swi¸atkowski function, Zeszyty Nauk. Politech. Ł´odz., Mat. 27 (1995), 87-93.
Search in Google Scholar
[7] MALISZEWSKI, A.: Maximums of Darboux quasi-continuous functions, Math. Slovaca 49 (1999), 381-386.
Search in Google Scholar
[8] MARCINIAK,M.-SZCZUKA,P.: On internally strong ´Swi¸atkowski functions (preprint).
Search in Google Scholar
[9] NATKANIEC, T.: On the maximum and the minimum of quasi-continuous functions, Math. Slovaca 42 (1992), 103-110.
Search in Google Scholar
[10] NATKANIEC, T.: On quasi-continuous functions having Darboux property, Math. Pannon. 3 (1992), 81-96.
Search in Google Scholar
[11] SZCZUKA, P.: Maximums of strong ´Swi¸atkowski functions, Math. Slovaca 52 (2002), 541-548.
Search in Google Scholar
[12] SZCZUKA, P.: Maximal classes for the family of strong ´Swi¸atkowski functions, RealAnal. Exchange 28 (2002/03), 429-437.10.14321/realanalexch.28.2.0429
Search in Google Scholar

DOI: https://doi.org/10.2478/v10127-012-0029-5 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

Journal RSS Feed

Language: English

Page range: 83 - 90

Published on: Nov 19, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Darboux function,

quasi-continuous function,

strong ´Swi¸atkowski function,

maximum of functions.

Related subjects:

Mathematics,

General mathematics

© 2012 Mariola Marciniak, Paulina Szczuka, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Previous article Volume 52 (2012): Issue 1 (August 2012)Next article