Strong Cauchy completeness in uniform frames.

We show that for uniform frames, with the underlying frame being Boolean, uniform paracompactness and strong Cauchy completeness are equivalent conditions. Certain aspects of uniform paracompactness are also considered. We then introduce the pointfree notion of preparacompactness and show that the completion of a preparacompact uniform frame is strongly Cauchy complete. We also formulate pointfree filter characterizations of Lindelöfness for regular frames in analogy to their classical topological counterparts. [ABSTRACT FROM AUTHOR]