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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.