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Remarks on I-density and I-approximately continuous functions. (English) Zbl 0587.54056

Starting with some definitions and results on I-density point, I-topology on the real line, \((\tau_ I)\), and I-approximately continuous functions, introduced by the authors themselves [A category analogue of the density topology, Fundam. Math. (to appear)], this note deals with other aspects concerning the I-density, (corollary 1), I-dispersion point, (theorem 1, lemmas 2 and 3), the family of \(\tau_ I\)-Borel sets, (theorem 3), \(\tau_ I\)-nowhere dense sets, (theorem 4), and I- approximately continuous functions, (theorem 5 and 7). Of course, the present note is a useful continuation of the authors’ work (loc. cit).
Reviewer: O.Costinescu

MSC:

54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
26A99 Functions of one variable
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