A Nagata-like theorem for certain function spaces |
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Authors: | Kevin M Drees |
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Institution: | 1. Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA
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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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