On a semicontinuous function

Abstract

Abstract. We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class is sufficiently rich to include all periods (integral of rational forms over algebraic cycles).

Effective decomposition of σ-continuous Borel functions

“…Any function with countably many points of discontinuity is σ-continuous. Such a function is of course of the first Baire class, but as reported by Keldysh [3], Novikov gave an example of a first Baire class function (actually an upper semicontinuous real valued function) which is not σ-continuous (see [7]). In fact "most" first Baire class functions are (in some natural sense) non-σ-continuous (see [5]).…”