Confluent Mappings and Arc Kelley Continua

The property of Kelley in nonmetric continua

The main purpose of this paper is to study the property of Kelley in nonmetric continua using inverse systems and limits.

Semi-terminal Continua in Kelley Spaces

A continuum K in a space X is said to be semi-terminal if at least one out of every two disjoint continua in X intersecting K is contained in K. Based on this concept, new structural results on Kelley continua are obtained. In particular, two decomposition theorems for Kelley continua are presented. One of these theorems is an improved version of the aposyndetic decomposition theorem for Kelley...

Mappings of Terminal Continua

Various kinds of nonseparating subcontinua were studied by a number of authors, see, for example, the expository paper [2], where a large amount of information on this subject is given. In the topological literature, or in continuum theory (to be more precise), the term “terminal,” when applied either to subcontinua of a given continuum or to points, and the same name “terminal” was assigned to...

On Quasi-ω-Confluent Mappings

Weakly Confluent Mappings and Finitely-generated Cohomology

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...