Abstract
Let X be a space, and let A be a zero-dimensional topological ring. In this paper we will consider a few natural questions that arise when studying the space C p (X, A), the ring of continuous functions from X to A, endowed with the topology of pointwise convergence. It will be shown that the zero-dimensionality of the codomain plays a vital role in this study. An upper and lower bound will be determined for the density of C p (X, A) using the density of A and the weight of X. The character of C p (X, A) will be computed, thus characterizing when C p (X, A) is metrizable. Lastly, we will consider the topological dual space of C p (X, A) and use it to prove a Nagata-like theorem.
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Presented by J. Martinez.
In memory of Paul F. Conrad
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Drees, K.M. A Nagata-like theorem for certain function spaces. Algebra Univers. 62, 259–272 (2009). https://doi.org/10.1007/s00012-010-0050-y
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DOI: https://doi.org/10.1007/s00012-010-0050-y