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 Cp(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 Cp(X, A) using the density of A and the weight of X. The character of Cp(X, A) will be computed, thus characterizing when Cp(X, A) is metrizable. Lastly, we will consider the topological dual space of Cp(X, A) and use it to prove a Nagata-like theorem.
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