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On Cantor manifolds for the small transfinite dimension

100%

Reńska M.

Commentationes Mathematicae

2006

tom 46

nr 2

We show that some of the spaces \(X_\alpha\) constructed in [7] are Cantor manifolds for the small transfinite dimension trind, which is transfinite extension of the Menger-Urysohn dimension. That gives us the construction of such spaces that is simpler than constructions of metrizable Cantor manifolds for trind published hitherto. In addition, our examples are disjoint unions of Euclidean cubes and the irrationals.

On partitions in cylinders over continua and a question of Krasinkiewicz

100%

Reńska M.

Colloquium Mathematicum

2011

tom 122

nr 2

203-214

We show that a metrizable continuum X is locally connected if and only if every partition in the cylinder over X between the bottom and the top of the cylinder contains a connected partition between these sets. J. Krasinkiewicz asked whether for every metrizable continuum X there exists a partiton L between the top and the bottom of the cylinder X × I such that L is a hereditarily indecomposable continuum. We answer this question in the negative. We also present a construction of such partitions for any continuum X which, for every ϵ > 0, admits a confluent ϵ -mapping onto a locally connected continuum.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Commentationes Mathematicae

2 Reńska M.

1 2011

1 2006

Wyniki wyszukiwania

On Cantor manifolds for the small transfinite dimension

On partitions in cylinders over continua and a question of Krasinkiewicz