Concerning atriodic tree-like continua

Exactly two-to-one maps from continua onto some tree-like continua

It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua ...

Concerning the Cut Points of Continua*

In this paper propositions will be established concerning the collection of all the cut points of a given planef continuum. It will be shown that there does not exist an uncountable collection of mutually exclusive subcontinua of a given continuum M each of which contains at least one cut point of M. With the aid of this fundamental theorem it is shown, among other things, that the set of all t...

Concerning Aposyndetic and Non-aposyndetic Continua

Introduction. One might judge from the title that I am going to discuss continua. For is not a continuum either aposyndetic or nonaposyndetic? What I intend to do is to consider continua from a certain point of view, and from this point of view continua may be classified in a rough sort of way. This system of classification (and the basic concept upon which it rests) is only in its infancy. Her...

CONCERNING INTERSECTING CONTINUA BY R. L. MooRu

Concerning the Spans of Certain Plane Separating Continua

Let X be a plane separating continuum. Suppose C is a convex space contained in a bounded component of R2 − X. It is shown that the span of the boundary of C is a lower bound for both the span and semispan of X. It is also shown that if a span of X is equal to the breadth of X and Y satisfies certain conditions relative to X then that span of X is an upper bound for the corresponding span of Y .