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Products of Świa̧tkowski functions

  • Aleksander Maliszewski EMAIL logo and Julia Wódka
Published/Copyright: August 17, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 3

Abstract

The aim of this paper is to characterize the products of Świa̧tkowski functions.

MSC 2010: Primary 26A21; Secondary 26A15, 54C08, 54C30
Key words: Świa̧tkowski function; quasi-continuous function; product of functions

(Communicated by Ján Borsík)

References

[1] Borsík, J.: Products of simply continuous and quasicontinuous functions, Math. Slovaca 45 (1995), 445–452. http://dml.cz/bitstream/handle/10338.dmlcz/136657/MathSlov_45-1995-4_13.pdfSearch in Google Scholar

[2] Kempisty, S.: Sur les fonctions quasicontinues, Fund. Math. 19 (1932), 184–197. http://matwbn.icm.edu.pl/ksiazki/fm/fm19/fm19115.pdf10.4064/fm-19-1-184-197Search in Google Scholar

[3] Maliszewski, A.: On the limits of strong Świa̧tkowski functions, Zeszyty Nauk. Politech. Łóodz. Mat. 27 (1995), No. 719, 87–93.Search in Google Scholar

[4] Maliszewski, A.: Sums and products of quasi-continuous functions, Real Anal. Exchange 21 (1995-96), 320–329. http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rae/134134324910.2307/44153922Search in Google Scholar

[5] Maliszewski, A.: Darboux Property and Quasi-continuity. A Uniform Approach, WSP, Słupsk, 1996.Search in Google Scholar

[6] Mańk, T.—Świa̧tkowski, T.: On some class of functions with Darboux’s characteristic, Zeszyty Nauk. Politech. Łóodz. Mat. 11 (1977), No. 301, 5–10.Search in Google Scholar

[7] Natkaniec, T.: Products of quasi-continuous functions, Math. Slovaca 40 (1990), 401–405. http://dml.cz/bitstream/handle/10338.dmlcz/129385/MathSlov_40-1990-4_7.pdfSearch in Google Scholar

[8] Pawlak, R. J.: Przekształcenia Darboux. Dissertation, Łódź University, 1985 (Polish).Search in Google Scholar

[9] Pawlak, H.—Wilczyński, W.: On the condition of Darboux and Świa̧tkowski for functions of two variables, Zeszyty Nauk. Politech. Łóodz. Mat. 15 (1982), No. 395, 31–35.Search in Google Scholar

[10] Szczuka, P.: Algebraiczne własności funkcji, któore spełniaja̧ silny warunek Świa̧tkowskiego. Ph.D. Thesis, PŁ, ŁŃdź, 2005 (Polish).Search in Google Scholar

[11] Szczuka, P.: Maximum of extra strong Świa̧tkowski functions, Math. Slovaca 62 (2012), 473–478. http://link.springer.com/article/10.2478%2Fs12175-012-0023-z10.2478/s12175-012-0023-zSearch in Google Scholar

[12] Thielman, H. P.: Types of functions, Amer. Math. Monthly 60 (1953), 156–161.10.1080/00029890.1953.11988260Search in Google Scholar

Received: 2013-8-2
Accepted: 2013-10-20
Published Online: 2016-8-17
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0163
Keywords for this article
Świa̧tkowski function; quasi-continuous function; product of functions

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  3. Research Article
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  5. Research Article
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  9. Research Article
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  11. Research Article
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