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Rectangularity Versus Piecewise Rectangularity of Product Spaces

Published online by Cambridge University Press:  20 November 2018

Kôichi Tsuda
Kôichi Tsuda*
Affiliation:
Department of Mathematics, Ehime University, Matsuyama 790, Japan
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Abstract

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We shall discuss relations between rectangularity and piecewise rectangularity of product spaces. In particular, we show that for each positive integer n there exists an n-dimensional, collectionwise normal, non-piecewise rectangular product X × Y which satisfies the inequality dim (X × Y) ≤ dim X + dim Y.

Keywords

54D2054F45Covering dimensionnormalitypiecewise rectangularityproduct spacestrongly 0-dimensionalityrectangularity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 1 , 01 March 1987 , pp. 49 - 56
Copyright
Copyright © Canadian Mathematical Society 01

References

1. Borges, C. J., On stratifiable spaces, Pacific J. Math. 17 (1966), 1–16.Google Scholar
2. Chiba, T. and Chiba, K., Q-paracompactness and closed mappings, Sci. Rep. Tokyo Kyoiku Daigaku 11 (1972), 231–234.Google Scholar
3. Chiba, T., A note on normally of product spaces, ibid. 12 (1974), 165–173.Google Scholar
4. Chiba, K., Two remarks on the normality of product spaces, Rep. Fac. Sci. Shizuoka Univ. 11 (1976), 17–22.Google Scholar
5. Chiba, K., Przymusinski, T.C. and Rudin, M.E., Normality of products and Morita's conjectures, preprint.Google Scholar
6. Engelking, R., General Topology (PWN, Warsaw, 1977).Google Scholar
7. Engelking, R., Dimension Theory (North-Holland, Amsterdam, 1978).Google Scholar
8. Filippov, V.V., On normally situated subspaces (Russian), Trundy Mat. Inst. Steklov AN SSSR 154 (1983), 239–251.Google Scholar
9. Hoshina, T. and Morita, K., On rectangular products of topological spaces, Top. Appl. 11 (1980), 47–57.Google Scholar
10. Morita, K., On the dimension of the product of topological spaces, Tsukuba J. Math. 1 (1977), 1—6.Google Scholar
11. Ohta, H., On normal, non-rectangular products, Quart. J. Math. Oxford (2), 32 (1981), 339–344.Google Scholar
12. Pasynkov, B.A., The dimension of products of normal spaces, Dokl. Akad. Nauk SSSR 209 (1973), 792-794 = Soviet Math. Dokl. 14 (1973), 530-533.Google Scholar
13. Pasynkov, B.A., On the dimension of rectangular products, Dokl. Akad. Nauk SSSR 221 (1975), 291-294 = Soviet Math. Dokl. 16 (1975), 344–347.Google Scholar
14. Pasynkov, B.A., Factorization theorems in dimension theory, Uspekhi Mat. Nauk 36 (1981), 147-175 = Russian Math. Surveys 36 (1981), 175-209.Google Scholar
15. Pasynkov, B.A., On the monotonicity of dimension, Dokl. Akad. Nauk SSSR 267 (1982), 548-552 = Soviet Math. Dokl. 26 (1982), 654-658.Google Scholar
16. Pasynkov, B.A., On dimension theory, in: James, I.M. and Kronheimer, E. (ed.) Aspects of Topology (In memory of Hugh Dowker 1912-1982), London Math. Soc. Lecture Note Ser. 93 (1985), 227–250.Google Scholar
17. Przymusiński, T.C., On the dimension of product spaces and an example of M. Wage, Proc. Amer. Math. Soc. 76(1979), 315-321.Google Scholar
18. Przymusiński, T.C., Product spaces, in: Reed, G.M. (ed.) Surveys in General Topology (Academic Press, New York) (1980), 399–429.Google Scholar
19. Przymusiński, T.C., A solution to a problem ofE. Michael, Pacific J. Math. 114 (1984), 235-242.Google Scholar
20. Steen, L.A. and Seebach, J.A., Jr., Counterexamples in topology 2nd. ed. (Springer-Verlag, New York, 1978).Google Scholar
21. Tamano, K., A note on E. Michael's example and rectangular products, J. Math. Soc. Japan 34 (1982), 187–190.Google Scholar
22. Terasawa, J., On the zero-dimensionality of some non-normal product spaces, Sci. Rep. Tokyo Kyoiku Daigaku 11 (1972), 95–102.Google Scholar
23. Tsuda, K., Some examples concerning the dimension of product spaces, Math. Japonica 27 (1982), 177–195.Google Scholar
24. Tsuda, K., An n-dimensional version of Wage's example, Colloq. Math. 49 (1984), 15—19.Google Scholar
25. Wage, M., The dimension of product spaces, preprint 1976, Department of Mathematics, Yale University.Google Scholar
26. Wage, M., The dimension of product spaces, Proc. Natl. Acad. Sci. U.S.A. 75 (1978), 4671–4672.Google Scholar