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Arcwise accessibility in hyperspaces

Sam B. Nadler, Jr. — 1976

CONTENTS1. Introduction........................................................................................................ 52. Segmentwise accessibility..................................................................................... 73. Arcwise accessibility of singletons....................................................................... 84. Compacta in X which arcwise disconnect 2 X or C(X)................................ 155. Hereditary indecomposability and arcwise accessibility.....................................

Absolute n-fold hyperspace suspensions

Sergio Macías;  Sam B. Nadler, Jr. — 2006

Colloquium Mathematicae

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 suspensions...

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