Baire one functions and their sets of discontinuity
نویسندگان
چکیده
منابع مشابه
Functions Whose Composition with Baire Class One Functions Are Baire Class One
We study the functions whose composition with Baire class one functions are Baire class one functions. We first prove some characterizations of such functions, then investigate a subclass of such functions which are defined in a natural way.
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We find a characterization of those Polish ultrametric spaces on which each Baire one function is first return recoverable. The notion of pseudo-convergence originating in the theory of valuation fields plays a crucial role in the characterization.
متن کاملConnectivity of diagonal products of Baire one functions
We characterize those Baire one functions f for which the diagonal product x 7→ (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.
متن کاملDecomposing Borel Sets and Functions and the Structure of Baire Class 1 Functions
All spaces considered are metric separable and are denoted usually by the letters X, Y , or Z. ω stands for the set of all natural numbers. If a metric separable space is additionally complete, we call it Polish; if it is a continuous image of ω or, equivalently, of a Polish space, it is called Souslin. The main subject of the present paper is the structure of Baire class 1 functions. Recent de...
متن کاملOn the Products of Bounded Dar- Boux Baire One Functions
It is shown that for each k > 1, if f is a Baire one function and f is the product of k bounded Darboux (quasi–continuous) functions, then f is the product of k bounded Darboux (quasi–continuous) Baire one functions as well.
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2016
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2016.9