A note on infinite-dimension under refinable maps
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- by Hisao Kato
- Proc. Amer. Math. Soc. 88 (1983), 177-180
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691304-6
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Abstract:
It is shown that refinable maps preserve weak infinite-dimension, but not strong infinite-dimension.References
- Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
- Jo Ford and J. W. Rogers Jr., Refinable maps, Colloq. Math. 39 (1978), no. 2, 263–269. MR 522365, DOI 10.4064/cm-39-2-263-269 W. Hurewicz and H. Wallman, Dimension theory, Van Nostrand, Princeton, N. J., 1948.
- Hisao Kato, Refinable maps in the theory of shape, Fund. Math. 113 (1981), no. 2, 119–129. MR 640617, DOI 10.4064/fm-113-2-119-129 I. Lončar and S. Mardešic, A note on inverse sequences of ANRs, Glasnik Math. 23 (1968), 41-48. P. R. Patten, Images of absolute neighborhood retracts and generalized absolute neighborhood retracts under refinable maps, Dissertation, University of Oklahoma, 1978.
- Roman Pol, A weakly infinite-dimensional compactum which is not countable-dimensional, Proc. Amer. Math. Soc. 82 (1981), no. 4, 634–636. MR 614892, DOI 10.1090/S0002-9939-1981-0614892-2
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 177-180
- MSC: Primary 54F45; Secondary 54C10
- DOI: https://doi.org/10.1090/S0002-9939-1983-0691304-6
- MathSciNet review: 691304