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Journals and Conferences
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.
In previous papers, [Barr, Burgess, & Raphael (2003), Barr, Raphael, & Woods (to appear)], two of us have investigated the situation of a topological space Y and a subspace X such that the induced map C(Y ) // C(X) is an epimorphism in the category CR of commutative rings (with units). We call such an embedding a CR -epic embedding and we say that X is… (More)
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)
This paper defines a solution manifold and a stable submanifold for a system of differential equations. Although we eventually work in the smooth topos, the first two sections do not mention topos theory and should be of interest to non-topos theorists. The paper characterizes solutions in terms of barriers to growth and defines solutions in what are called… (More)
We study and, in a number of cases, classify completely the limit closures in the category of commutative rings of subcategories of integral domains.
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)
Let R be a commutative ring whose complete ring of quotients is Rinjective. We show that the category of topological R-modules contains a full subcategory that is ∗-autonomous using R itself as dualizing object. In order to do this, we develop a new variation on the category chu(D, R), where D is the category of discrete R-modules: the high wide… (More)
In [Barr & Kleisli 2001] we described ?-autonomous structures on two full subcategories of topological abelian groups. In this paper we do the same for sup semilattices except that uniform structures play the role that topology did in the earlier paper.