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2 Bulletin of the Polish Academy of Sciences. Mathematics

2 Makuchowski W.

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On local n-connectedness in hyperspaces

Makuchowski W.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 1

29-33

It is shown that for any compact metric space X in hyperspaces C(X) of subcontinua of X and 2[sup X] of all nonempty closed subsets of X, local connectedness and local n-connectedness are equivalent at any point.

On local connectedness in hyperspaces

Makuchowski W.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 2

119-126

It is shown that for any Hausdorff compactum X in the hyperspace C(X) of subcontinua of X (in the hyperspace 2^X of all nonempty closed subsets of X) local connectedness and local arcwise connectedness are equivalent at any point. If X has the property of Kelley, then local connectedness of C(X) is proved to be equivalent to some stronger kinds of local connectedness and of local arcwise connectedness.