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2 Bulletin of the Polish Academy of Sciences. Mathematics

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An exactly two-to-one map from an indecomposable chainable continuum

Krzempek J.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 3

335-339

It is shown that a certain indecomposable chainable continuum is the domain of an exactly two-to-one continuous map. This answers a question of Jo W. Heath.

Another approach to dimension of maps

Krzempek J.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 2

141-154

Two equivalent definitions of the Cech-Lebesgue dimension are extended to closed (continuous) maps. This leads to two different dimension-like functions: the covering dimension and partition dimension of maps. A few characterizations of at most n-dimensional maps (for both dimensions) are proved as well as countable and locally finite sum theorems.