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Ideas and influence of Karol Borsuk

Dydak J.

Wiadomości Matematyczne

2012

T. 48, Nr 2

81--95

Strong cohomological dimension

Dydak J., Koyama A.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

Vol. 56, no 2

183-189

We characterize strong cohomological dimension of separable metric spaces in terms of extension of mappings. Using this characterization, we discuss the relation between strong cohomological dimension and (ordinal) cohomological dimension and give examples to clarify their gaps. We also show that Inde X = dim[sub G] X if X is a separable metric ANR and G is a countable Abelian group. Hence dim[sub Z] X = dim X for any separable metric ANR X.

Compacta not embeddable into Cartesian products of curves

Dydak J., Koyama A.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 1

51-56

We prove that an n-dimensional compactum X cannot be embedded into the Cartesian product of n curves if there is a group G such that [H^1] (X;G) = 0 and [H^n](X;G) [is not equal to] O.