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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. 1 Introduction It is well known that a product… (More)

- David Joyce, John Kennison, +4 authors Nicholas S. Thompson
- J. Artificial Societies and Social Simulation
- 2006

- MICHAEL BARR, JOHN F. KENNISON, ©Michael Barr, John F. Kennison
- 2005

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)

- JOHN F. KENNISON
- 2002

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)

- JOHN F. KENNISON
- 2006

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)

- JOHN F. KENNISON
- 2009

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)

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)

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)

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)

We study and, in a number of cases, classify completely the limit closures in the category of commutative rings of subcategories of integral domains.