On the uniqueness of the decomposition of continua into Cartesian products

• Autorzy: Rosicki W.
• Języki publikacji: EN

Abstrakty

EN

There exist two 2-dimensional continua such that they are not homeomorphic but their Cartesian squares are homeomorphic. There exist two 2-dimensional continua such that they are not homeomorphic but their Cartesian products with 1-dimensional continuum different from an arc are homeomorphic.

Słowa kluczowe

EN

product Cartesian; continuum

PL

iloczyn kartezjański; continuum

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2003
• Tom: Vol. 51, no 3
• Strony: 247--250
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Rosicki W.

• Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 81-952 Gdańsk, Poland,

Bibliografia

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• [2] W. W. Comfort, K.-H. Hofmann, D. Remus, Topological groups and Semigroups, in: Recent progress in general topology, eds. M. Hušek, J. van Mill, North-Holland, Amsterdam London New York Tokyo 1992, 57-144.
• [3] L. Fuchs, Infinite abelian groups, Academic Press, New York London 1973.
• [4] L. Fuchs, F. Loonstra, Ondirect decompositions of torsion-free abelian groups of finite rank, Rend. Sem. Mat. Univ. Padova, 44 (1970) 75-83.
• [5] R. H. Fox, On a problem of S.Ulam concerning Cartesian products, Fund. Math., 34 (1947) 278-287.
• [6] K. H. Hofman, P. S. Mostert, Cohomology theories of compact abelian groups, Dt. Verl. d. Wiss, Berlin and Springer-Verlag, Berlin.
• [7] S. Kwasik, R. Schultz, All Zp lens spaces have diffeomorphic squares, Topology 41 (2002) 321-340.
• [8] L. S. Pontryagin, Topological groups, Gordon and Breach Sci. Pub., Inc., New York London Paris 1966.
• [9] W. Rosicki, On a problem of S. Ulam concerning Cartesian squares of 2-polyhedra, Fund. Math., 127 (1986) 101-125.
• [10] W. Rosicki, On Cartesian powers of 2-polyhedra, Coll. Math., 59 (1990) 141-149.
• [11] W. Rosicki, On decomposition of 3-polyhedra into a Cartesian product, Fund. Math., 136 (1990) 53-63.
• [12] S. Ulam, Problem 56, Fund. Math., 20 (1933) 285.