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We answer positively two questions from [3, Remark on page 165], concerning the coincidence of small and large inductive dimensions ind and Ind in the class of order totally paracompact spaces.
Wydawca
Rocznik
Tom
Strony
255--265
Opis fizyczny
Bibliogr. 14 poz.
Twórcy
autor
- Department of Mathematics, Linkeping University, 581 83 Linkeping, Sweden
autor
- Department of Mathematics, Shimane University, Matsue, Shimane, 690-8504 Japan
Bibliografia
- [1] D. K. Burke, Covering properties, in: Handbook of set-theoretic topology, eds.: K. Kunen and J. E. Vaughan, North-Holland, Amsterdam (1993) 347-422.
- [2] V. A. Chatyrko, K. L. Kozlov, On (transfinite) small inductive dimension of product, Comment. Math. Univ. Carolin., 41 (3) (2000) 597-603.
- [3] R. Engelking, Theory of dimensions, finite and infinite, Heldermann Verlag, Lemgo 1995.
- [4] B. Fitzpatrick Jr., R. M. Ford, On the equivalence of small and large inductive dimension in certain metric spaces, Duke Math. J., 34 (1967) 33-37.
- [5] J. A. French, Some completely normal spaces in which small and large inductive dimension coincide, Houston J. Math., 2 (1976) 181-193.
- [6] V. V. Filippov, A bicompactum with noncoinciding inductive dimensions, Sov. Math. Dokl., 10 (1969) 208-211.
- [7] V. V. Filippov, On inductive dimension of product of compact spaces, Sov. Math. Dokl., 13 (1972) 250-254.
- [8] J. Kulesza, Metrizable spaces where the inductive dimensions disagree, Trans. Amer Math. Soc., 318 (1990) 763-781.
- [9] T. Mizokami, The equality of large and small inductive dimensions, J. London Math. Soc. (2), 20 (1979) 541-543.
- [10] K. Nagami, A note on the large inductive dimension of totally normal spaces, J. Math. Soc. Japan, 21 (1969) 282-290.
- [11] K. Nagami, Correction to “A note on the large inductive dimension of totally normal spaces”, (J. Math. Soc. Japan, 21 (1969) 282-290), J. Math. Soc. Japan, 25 (1973) 733.
- [12] B. A. Pasynkov, K. Tsuda, Product theorems in dimension theory, Tsukuba J. Math., 17 (1993) 59-70.
- [13] P. Roy, Nonequality of dimensions for metric spaces, Trans. Amer. Math. Soc., 134 (1968) 117-132.
- [14] A. V. Zarelua, On a theorem of Hurewicz, Amer. Math. Soc. Transl., 55 (2) (1966) 141-152.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT2-0001-1176
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