A Note: To the Sierpiński First Class of Functions

Author:

Menkyna Robert1

Affiliation:

1. Institute of Aurel Stodola, Faculty of Electrical Engineering , University of Žilina , ul. kpt. J. Nálepku 1390, SK–031-01 Liptovský Mikuláš, Slovakia

Abstract

Abstract The purpose of this paper is to establish some theorems concerning approximation and representation of a function of the Sierpiński first class by Darboux function of the Sierpiński first class.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference16 articles.

1. [1] BRUCKNER, A. M.: Differentiation of Real Functions, in: Lecture Notes in Math., Vol. 659, Springer, Berlin, 1978.

2. [2] BRUCKNER, A. M.—CEDER, J. G.—KESTON, R.: Representations and approximations by Darboux functions in the first class of Baire, Rev. Roum. Math. Pures Appl. 9 (1968), 1247–1254.

3. [3] GUREVIČ, A. B.: D-continuous Sierpiński components, Dokl. Akad. Nauk BSSR 10 (1966), 539–571. (In Russian)

4. [4] KEMPISTY, S.: Sur les functions quasicontinues, Fund. Math. 19 (1932), 184–197.

5. [5] MALISZEWSKI, A.: Darboux Property and Quasi-Continuity: A Uniform Approach. Wydaw. Uczelniane WSP, 1996.

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