Array convergence of functions of the first Baire class

Author:
Helmut Knaust

Journal:
Proc. Amer. Math. Soc. **112** (1991), 529-532

MSC:
Primary 46E15; Secondary 46B15

MathSciNet review:
1057955

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that every array of elements in a pointwise compact subset of the Baire- functions on a Polish space, whose iterated pointwise limit exists, is converging Ramsey-uniformly. An array in a Hausdorff space is said to converge Ramsey-uniformly to some in , if every subsequence of the positive integers has a further subsequence such that every open neighborhood of in contains all elements with except for finitely many .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1057955-9

Keywords:
First Baire class,
array convergence,
Ramsey theory

Article copyright:
© Copyright 1991
American Mathematical Society