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Proceedings of the American Mathematical Society

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Products of infinite-dimensional spaces

Author: Dale M. Rohm
Journal: Proc. Amer. Math. Soc. 108 (1990), 1019-1023
MSC: Primary 54F45; Secondary 54B10, 57N20
MathSciNet review: 946625
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Abstract: Observations concerning the product of R. Pol's weakly infinite-dimensional uncountable-dimensional compactum with various spaces are made. A proof showing that the product of a $ C$-space and a compact $ C$-space is again a $ C$-space is given. Related questions, motivated by this result, are asked.

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  • [AG] D. F. Addis and J. H. Gresham, A class of infinite-dimensional spaces. Part I: Dimension theory and Alexandroff's problem, Fund. Math. 101 (1978), 195-205. MR 521122 (80b:54041)
  • [E1] R. Engelking, Dimension theory, North-Holland, Amsterdam, Polish Scientific Publishers, Warszaw, 1978. MR 0482697 (58:2753b)
  • [E2] -, Transfinite dimension theory, Surveys in Gen. Top., Academic Press, New York, 1978, 131-161. MR 564101 (81g:54036)
  • [EP] R. Engelking and E. Pol, Countable-dimensional spaces: a survey, Dissert. Math. 216 (1983), 1-41. MR 722011 (85f:54075)
  • [G] D. J. Garity, Property $ C$ and closed maps, Topol. Appl. 26 (1987), 125-130. MR 896868 (88e:54048)
  • [H] W. E. Haver, A covering property for metric spaces, in Topology, Conf., Virginia Polytechnic Institute and State University, R. E. Diockman and P. Fletcher, eds., Lecture Notes in Math. vol. 375, Springer-Verlag, New York, 1974, 108-113. MR 0365504 (51:1756)
  • [P] E. Pol, A weakly infinite-dimensional space whose product with the irrationals is strongly infinite-dimensional, Proc. Amer. Math. Soc. 98 (1986), 349-352. MR 854045 (88a:54083)
  • [P1] R. Pol, A weakly infinite-dimensional compactum which is not countable-dimensional, Proc. Amer. Math. Soc. 82 (1981), 634-636. MR 614892 (82f:54059)
  • [P2] -, A remark on $ A$-weakly infinite-dimensional spaces, Topology Appl. 13 (1982), 97-101. MR 637431 (83b:54051)

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Keywords: Property $ C$, weakly infinite-dimensional spaces, countable-dimensional spaces, product spaces
Article copyright: © Copyright 1990 American Mathematical Society

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