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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Descriptive complexity of function spaces


Authors: D. Lutzer, J. van Mill and R. Pol
Journal: Trans. Amer. Math. Soc. 291 (1985), 121-128
MSC: Primary 54C35; Secondary 03E15, 04A15, 54H99
MathSciNet review: 797049
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Abstract: In this paper we show that $ {C_\pi }(X)$, the set of continuous, real-valued functions on $ X$ topologized by the pointwise convergence topology, can have arbitrarily high Borel or projective complexity in $ {{\mathbf{R}}^X}$ even when $ X$ is a countable regular space with a unique limit point. In addition we show how to construct countable regular spaces $ X$ for which $ {C_\pi }(X)$ lies nowhere in the projective hierarchy of the complete separable metric space $ {{\mathbf{R}}^X}$.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0797049-2
PII: S 0002-9947(1985)0797049-2
Article copyright: © Copyright 1985 American Mathematical Society