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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.

α -continuous and α -irresolute multifunctions

Jiling Cao, Ivan L. Reilly (1996)

Mathematica Bohemica

Recently Popa and Noiri [10] established some new characterizations and basic properties of α -continuous multifunctions. In this paper, we improve some of their results and examine further properties of α -continuous and α -irresolute multifunctions. We also make corrections to some theorems of Neubrunn [7].

Σ -products and selections of set-valued mappings

Ivailo Shishkov (2001)

Commentationes Mathematicae Universitatis Carolinae

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 Y , where X is a Σ -product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

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