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Topologies And Cotopologies Generated By Sets Of Functions, Alan Dow, Melvin Henriksen, Ralph Kopperman, R. G. Woods

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Let L be either [0, 1] or {0, 1} with the usual order. We study topologies on a set X for which the cozero-sets of certain subfamilies H of L^x form a base, and the properties imposed on such topologies by hypothesizing various order-theoretic conditions on H. We thereby obtain useful generalizations of extremely disconnected spaces, basically disconnected spaces, and F-spaces. In particular we use these tools to study the space of minimal prime ideals of certain commutative rings.