Displaying similar documents to “A generalization of a theorem of Skala”

Hyperspaces of Peano continua of euclidean spaces

Helma Gladdines, Jan van Mill (1993)

Fundamenta Mathematicae

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If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space L ( ℝ n ) is homeomorphic to B ∞ , where B denotes the pseudo-boundary of the Hilbert cube Q.

Absolute n-fold hyperspace suspensions

Sergio Macías, Sam B. Nadler, Jr. (2006)

Colloquium Mathematicae

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The notion of an absolute n-fold hyperspace suspension is introduced. It is proved that these hyperspaces are unicoherent Peano continua and are dimensionally homogeneous. It is shown that the 2-sphere is the only finite-dimensional absolute 1-fold hyperspace suspension. Furthermore, it is shown that there are only two possible finite-dimensional absolute n-fold hyperspace suspensions for each n ≥ 3 and none when n = 2. Finally, it is shown that infinite-dimensional absolute n-fold hyperspace...