On the product of two functions which are approximately continuous and approximately regulated

• Autorzy: Grande M.
• Języki publikacji: EN

Abstrakty

EN

In this article we investigate the products of two unilaterally approximately continuous and simultaneously approximately regulated functions. In particular we prove some necessary conditions satisfied by the products of two such functions and a sufficient condition ensuring that a function is the product of two such functions.

Słowa kluczowe

EN

approximately regulated function; steplike functions; density topology; unilateral approximate continuity

PL

funkcje aproksymacyjne; funkcje przybliżone; przestrzeń topologiczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 2
• Strony: 327--334
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Grande M.

• Institute of Mathematics Bydgoszcz Academy Pl. Weyssenhoffa 11, 85-072 Bydgoszcz, Poland

Bibliografia

• [1] S. K. Berberian, Regulated functions: Bourbaki's alternative to the Riemann integral, Amer. Math. Monthly 86 No. 3 (1979), 208-211.
• [2] A. M. Bruckner, Differentiation of Real Functions, Lectures Notes in Mathematics 659, Springer-Verlag, Berlin Heidelberg New York 1978.
• [3] C. Goffmam, G. Moran, D. Waterman, The structure of regulated functions, Proc. Amer. Math. Soc. 57 No. 1 (1976), 61-65.
• [4] M. Grande, On the sums of unilaterally continuous jump functions, Demonstratio Math. Vol. XXXV, No. 4 (2002), 743-748.
• [5] M. Grande, On the sums of unilaterally approximately continuous and approximate jump functions, Real Anal. Exchange 28 No.2 (2002-2003), 623-630.
• [6] M. Grande, On the products of unilaterally continuous regulated functions, in preparation.
• [7] G. Moran, On regulated and steplike functions, Trans. Amer. Math. Soc. 231 No. 1 (1977), 249-257.
• [8] F. D. Tall, The density topology, Pacific J. Math. 62 (1976), pp. 275-284.
• [9] Z. Zahorski, Sur la premiere derivee, Trans. Amer. Math. Soc. 69 (1950), pp. 1-54.