Note on Compact Sets of First Baire Class Functions
نویسندگان
چکیده
منابع مشابه
Compact Subsets of the First Baire Class
Perhaps the earliest results about pointwise compact sets of Baire class-1 functions are the two selection theorems of E. Helly found in most of the standard texts on real variable (see, e.g., [Lo], [N]). These two theorems are really theorems about a particular example of a compact set of Baire class-1 functions known today as Helly space, the space of all nondecreasing functions from the unit...
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Let X be a Polish space and K a separable compact subset of the first Baire class on X. For every sequence f = (fn)n dense in K, the descriptive set-theoretic properties of the set Lf = {L ∈ [N] : (fn)n∈L is pointwise convergent} are analyzed. It is shown that if K is not first countable, then Lf is Π 1 1 complete. This can also happen even if K is a pre-metric compactum of degree at most two, ...
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In 1990 Kechris and Louveau developed the theory of three very natural ranks on the Baire class 1 functions. A rank is a function assigning countable ordinals to certain objects, typically measuring their complexity. We extend this theory to the case of Baire class ξ functions, and generalize most of the results from the Baire class 1 case. We also show that their assumption of the compactness ...
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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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.2307/2045670