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

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)

- 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)

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)

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)

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.