Array convergence of functions of the first Baire class
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- by Helmut Knaust PDF
- Proc. Amer. Math. Soc. 112 (1991), 529-532 Request permission
Abstract:
We show that every array $(x(i,j):1 \leq i < j < \infty )$ of elements in a pointwise compact subset of the Baire-$1$ functions on a Polish space, whose iterated pointwise limit ${\lim _i}{\lim _j}x(i,j)$ exists, is converging Ramsey-uniformly. An array $(x{(i,j)_{i < j}})$ in a Hausdorff space $T$ is said to converge Ramsey-uniformly to some $x$ in $T$, if every subsequence of the positive integers has a further subsequence $({m_i})$ such that every open neighborhood $U$ of $x$ in $T$ contains all elements $x({m_i},{m_j})$ with $i < j$ except for finitely many $i$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 529-532
- MSC: Primary 46E15; Secondary 46B15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1057955-9
- MathSciNet review: 1057955