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2 Bulletin of the Polish Academy of Sciences. Mathematics

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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.

Topological characterization of finite mappings

Jelonek Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2001

Vol. 49, no 3

279-283

In the paper [4] Krasiński and Spodzieja proved that if f : X -> Y is a Zariski closed non-constant mapping of affine varieties over C (where dim X [is greater than or equal to] 2), then f is finite. In this paper we generalize this result to the case of arbitrary algebraically closed field.