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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Finite extensions of mappings of finite sets

Karaś M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 2

237-239

In this note we prove that for every finite sets V, W [is a subset of] [C^k] with k, #V, #W > 1 and for every surjective mapping f : V --> W there exists a finite mapping F : [C^k] --> [C^k] such that F\v = f, gdegF = gdegf and degF [is less than or equal to (#V - 1)^2].

On some characterization of proper polynomial mappings

Rodak T., Spodzieja S.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 2

157-164

It is well known that a proper, in the classical topology, polynomial mapping is closed in the Zariski topology. In the paper we prove that the inverse is true. Namely, any non-constant polynomial mapping from [C^n] into [C^m] which is closed in the Zariski topology is proper in the classical topology.