Concerning upper semicontinuous decompositions of irreducible continua.

Decompositions of Continua over the Hyperbolic Plane

The following theorem is proved. THEOREM. Let X be a homogeneous continuum such that Hl(X) ^ 0. Ij'$/ is the collection of maximal terminal proper subcontinua of X, then (1) The collection ff is a monotone, continuous, terminal decomposition ofX, (2) The nondegenerate elements of%? are mutually homeomorphic, indecomposable, cell-like, terminal, homogeneous continua of the same dimension as X, (...

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...

Iterative roots of upper semicontinuous multifunctions

*Correspondence: [email protected] Department of Mathematics, Binzhou University, Shandong, 256603, P.R. China Abstract The square iterative roots for strictly monotonic and upper semicontinuous functions with one set-valued point were fully described in (Li et al. in Publ. Math. (Debr.) 75:203-220, 2009). As a continuation, we study both strictly monotonic and nonmonotonic multifunctio...

CONCERNING INTERSECTING CONTINUA BY R. L. MooRu