A Pointfree Study of Bases For Spaces Of Minimal Prime Ideals

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Mathematics (HMC)

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Let C (X) denote the ring of all real-valued continuous functions on a topological space X, and mX its space of minimal prime ideals with the hull-kernel topology. It has a base consisting of clopen sets and which contains the closure of the union of any sequence of its members. In the paper Spaces with a pretty base ( J. Pure and Appl. Algebra 70 (1991), 81-87), spaces with a base with these properties are studied and are shown to have almost all of the known properties of the space mX including the fact that if it is a weakly Lindel¨ of space, then it is basically disconnected. In the present paper, analogous results are derived in a pointfree context in which topological spaces are replaced by frames. In some cases, we are able to obtain more general results with simpler proofs.

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© 2003 Taylor and Francis