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On Grande’s problem concerning $${\mathcal B}_ 1^*$$ functions. (English) Zbl 0839.26002
It is shown that in the definition of Baire one star functions continuity on open subsets (of arbitrary perfect sets) can be replaced by quasi-continuity on open subsets. This answers in the affirmative a question by Z. Grande who proved the analogous statement for Baire one functions and existence of points of quasi-continuity.

##### MSC:
 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 26A21 Classification of real functions; Baire classification of sets and functions
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##### References:
 [1] GRANDE Z.: Baire functions and their restrictions to special sets. Math. Slovaca) · Zbl 0839.26003 [2] KEMPISTY S.: Sur les fonctions semi-continues par rapport à chacune de deux variables. Fund. Math. 14 (1929), 237-241. · JFM 55.0145.05 [3] KIRCHHEIM B.: Baire one star functions. Real Anal. Exchange) · Zbl 0853.54018 [4] KURATOWSKI K.: Topology. Vol I. PWN, Warszawa, 1958. · Zbl 0158.40901 [5] LUKEŠ J., MALÝ J., ZAJÍČEK L.: Fine Topology Methods in Real Analysis and Potential Theory. Lecture Notes in Math. 1189, Springer, Berlin-New York, 1986. · Zbl 0607.31001 [6] O’MALLEY R. J.: Baire* 1, Darboux functions. Proc. Amer. Math. Soc. 60 (1976), 187-192. · Zbl 0339.26010
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