Spaces whose $n$th power is weakly infinite-dimensional but whose $(n+1)$th power is not
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- by Elżbieta Pol PDF
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Abstract:
For every natural number $n$ we construct a metrizable separable space $Y$ such that ${Y^n}$ is weakly infinite-dimensional (moreover, is a $C$-space) but ${Y^{n + 1}}$ is strongly infinite-dimensional.References
- K. Alster and P. Zenor, An example concerning the preservation of the Lindelöf property in product spaces, Set-theoretic topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975–1976) Academic Press, New York, 1977, pp. 1–10. MR 0442884
- Eric K. van Douwen, A technique for constructing honest locally compact submetrizable examples, Topology Appl. 47 (1992), no. 3, 179–201. MR 1192308, DOI 10.1016/0166-8641(92)90029-Y
- Ryszard Engelking and Elżbieta Pol, Countable-dimensional spaces: a survey, Dissertationes Math. (Rozprawy Mat.) 216 (1983), 41. MR 722011
- Dennis J. Garity, Property $C$ and closed maps, Topology Appl. 26 (1987), no. 2, 125–130. MR 896868, DOI 10.1016/0166-8641(87)90063-0
- Dennis J. Garity and Dale M. Rohm, Property C, refinable maps and dimension raising maps, Proc. Amer. Math. Soc. 98 (1986), no. 2, 336–340. MR 854043, DOI 10.1090/S0002-9939-1986-0854043-7
- Yasunao Hattori and Kohzo Yamada, Closed pre-images of $C$-spaces, Math. Japon. 34 (1989), no. 4, 555–561. MR 1005256
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751
- K. Kuratowski, Applications of the Baire-category method to the problem of independent sets, Fund. Math. 81 (1973), no. 1, 65–72. MR 339092, DOI 10.4064/fm-81-1-65-72
- E. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc. 69 (1963), 375–376. MR 152985, DOI 10.1090/S0002-9904-1963-10931-3
- Ernest A. Michael, Paracompactness and the Lindelöf property in finite and countable Cartesian products, Compositio Math. 23 (1971), 199–214. MR 287502
- Jan Mycielski, Almost every function is independent, Fund. Math. 81 (1973), no. 1, 43–48. MR 339091, DOI 10.4064/fm-81-1-43-48
- Elżbieta Pol, A weakly infinite-dimensional space whose product with the irrationals is strongly infinite-dimensional, Proc. Amer. Math. Soc. 98 (1986), no. 2, 349–352. MR 854045, DOI 10.1090/S0002-9939-1986-0854045-0
- 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
- Roman Pol, A remark on $A$-weakly infinite-dimensional spaces, Topology Appl. 13 (1982), no. 1, 97–101. MR 637431, DOI 10.1016/0166-8641(82)90011-6 —, Note on products of weakly infinite-dimensional spaces with Menger Property, preprint.
- Teodor C. Przymusiński, On the notion of $n$-cardinality, Proc. Amer. Math. Soc. 69 (1978), no. 2, 333–338. MR 491191, DOI 10.1090/S0002-9939-1978-0491191-3
- Teodor C. Przymusiński, Normality and paracompactness in finite and countable Cartesian products, Fund. Math. 105 (1979/80), no. 2, 87–104. MR 561584, DOI 10.4064/fm-105-2-87-104
- Dale M. Rohm, Products of infinite-dimensional spaces, Proc. Amer. Math. Soc. 108 (1990), no. 4, 1019–1023. MR 946625, DOI 10.1090/S0002-9939-1990-0946625-X
- Dale M. Rohm, Weakly infinite-dimensional product spaces, Proc. Amer. Math. Soc. 111 (1991), no. 1, 255–260. MR 1037221, DOI 10.1090/S0002-9939-1991-1037221-8
- Leonard R. Rubin, Noncompact hereditarily strongly infinite-dimensional spaces, Proc. Amer. Math. Soc. 79 (1980), no. 1, 153–154. MR 560602, DOI 10.1090/S0002-9939-1980-0560602-6
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 871-876
- MSC: Primary 54F45; Secondary 54B10
- DOI: https://doi.org/10.1090/S0002-9939-1993-1148027-5
- MathSciNet review: 1148027