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1/2-Homogeneous hyperspace suspensions

Sergio Macías, Patricia Pellicer-Covarrubias (2012)

Colloquium Mathematicae

We continue the study of 1/2-homogeneity of the hyperspace suspension of continua. We prove that if X is a decomposable continuum and its hyperspace suspension is 1/2-homogeneous, then X must be continuum chainable. We also characterize 1/2-homogeneity of the hyperspace suspension for several classes of continua, including: continua containing a free arc, atriodic and decomposable continua, and decomposable irreducible continua about a finite set.

A characterization of almost continuity and weak continuity

Chrisostomos Petalas, Theodoros Vidalis (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

It is well known that a function f from a space X into a space Y is continuous if and only if, for every set K in X the image of the closure of K under f is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets K of X .

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