John Kennison

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We study conditions on a topological space that guarantee that its product with every Lindelöf space is Lindelöf. The main tool is a condition discovered by K. Alster and we call spaces satisfying his condition Alster spaces. We also study some variations on scattered spaces that are relevant for this question.
We find the injective hulls of partially ordered monoids in the category whose objects are po-monoids and submultiplicative order-preserving functions. These injective hulls are with respect to a special class of monics called “embeddings”. We show as well that the injective objects with respect to these embeddings are precisely the quantales.
We continue our examination of absolute CR -epic spaces, or spaces with the property that any embedding induces an epimorphism, in the category of commutative rings, between their rings of continuous functions. We examine more closely the deleted plank construction, which generalizes the Dieudonné construction, and yields absolute CR -epic spaces which are(More)
A flow on a compact Hausdorff space X is given by a map t : X → X. The general goal of this paper is to find the “cyclic parts” of such a flow. To do this, we approximate (X, t) by a flow on a Stone space (that is, a totally disconnected, compact Hausdorff space). Such a flow can be examined by analyzing the resulting flow on the Boolean algebra of clopen(More)