Non-$n$-mutually aposyndetic continua

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...

SOME THEOREMS ON n-HOMOGENEOUS CONTINUA

Non-metric continua and multi-valued mappings

A continuum is an arboroid if it is hereditarily unicoherent and arcwise connected. A metric arboroid is a dendroid. A generalized dendrite is a locally connected arboroid. Among other things, we shall prove that a locally connected continuum X is a generalized dendrite if and only if X has the fixed point property for continuous, closed set-valued mappings.

On Continua Whose Links Are Non-intersecting

There are many examples known of compact continua no two of whose simple links intersect, even though uncountably many of the links are nondegenerate. On page 346 of his Foundations of point set theory [ l] , R. L. Moore has given an example of a compact continuum which is the sum of an uncountable collection of nondegenerate simple links, only a countable number of which intersect. In view of ...

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...