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. 1 Introduction It is well known that a product… (More)
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 absolute CR-epic if every embedding of X is CR-epic. We continue this investigation. Our most… (More)
This paper defines flows (or discrete dynamical systems) and cyclic flows in a category and investigates how the trajectories of a point might approach a cycle. The paper considers cyclic flows in the categories of Sets and of Boolean algebras and their duals and characterizes the Stone representation of a cyclic flow in Boolean algebras. A cyclic spectrum… (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)
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.
This paper reviews the basic properties of coherent spaces, characterizes them, and proves a theorem about countable meets of open sets. A number of examples of coherent spaces are given, including the set of all congruences (equipped with the Scott topology) of a model of a theory based on a set of partial operations. We also use an unpublished theorem of… (More)
This paper continues the work of our previous papers, The cyclic spectrum of a Boolean flow TAC 10 392-419 and Spectra of finitely generated Boolean flows TAC 16 434-459. We define eventually cyclic Boolean flows and the eventually cyclic spectrum of a Boolean flow. We show that this spectrum, as well as the spectra defined in our earlier papers, extend to… (More)
Let R be a commutative ring whose complete ring of quotients is R-injective. We show that the category of topological R-modules contains a full sub-category 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)
The purpose of this paper is to extend the results of [Barr et al. (2008), Section 8] from the case of abelian groups (Z-modules) to that of modules over a large class of not necessarily commutative rings.