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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.
Recently Popa and Noiri [10] established some new characterizations and basic properties of -continuous multifunctions. In this paper, we improve some of their results and examine further properties of -continuous and -irresolute multifunctions. We also make corrections to some theorems of Neubrunn [7].
Every lower semi-continuous closed-and-convex valued mapping , where is a -product of metrizable spaces and is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.
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