1. INTRODUCTION. In the past thirty or forty years inverse limits have been used extensively in dynamical systems as well as in continuum theory as a means to attack a myriad of unsolved problems. A study of one-dimensional branched manifolds by R. F. Williams [16] provided an early demonstration of the utility of the inverse limit construction in dynamical… (More)

In this article we define the inverse limit of an inverse sequence (X1, f1), (X2, f2), (X3, f3), . . . where each Xi is a compact Hausdorff space and each fi is an upper semi-continuous function from Xi+1 into 2i . Conditions are given under which the inverse limit is a Hausdorff continuum and examples are given to illustrate the nature of these inverse… (More)

The characterization of chainable continua as inverse limits on [0, 1] has resulted in many papers which have contributed to our knowledge of both inverse limits and chainable continua. Quite simple maps on [0, 1] give rise to quite complicated inverse limits. In this paper we begin an investigation of continua that can be represented by inverse limits of… (More)

A point p of a topological space X is a cut point of X if X −{p} is disconnected. Further, if X −{p} has precisely m components for some natural number m≥ 2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y , we will say that Y is a cut point space. Herein we construct a space S so that S is a connected… (More)

A point p of a topological space X is a cut point of X if X − {p} is disconnected. Further, if X −{p} has precisely m components for some natural number m ≥ 2 we will say that p has cut point order m. If each point y of a connected space Y is a cut point of Y , we will say that Y is a cut point space. Herein we construct a space S so that S is a connected… (More)