Products of infinite-dimensional spaces

Rohm, Dale M.

doi:10.1090/S0002-9939-1990-0946625-X

Products of infinite-dimensional spaces
HTML articles powered by AMS MathViewer

by Dale M. Rohm PDF

Proc. Amer. Math. Soc. 108 (1990), 1019-1023 Request permission

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.

References

David F. Addis and John H. Gresham, A class of infinite-dimensional spaces. I. Dimension theory and Alexandroff’s problem, Fund. Math. 101 (1978), no. 3, 195–205. MR 521122, DOI 10.4064/fm-101-3-195-205
Ryszard Engelking, Teoria wymiaru, Biblioteka Matematyczna, Tom 51. [Mathematics Library, Vol. 51], Państwowe Wydawnictwo Naukowe, Warsaw, 1977 (Polish). MR 0482696
R. Engelking, Transfinite dimension, Surveys in general topology, Academic Press, New York-London-Toronto, Ont., 1980, pp. 131–161. MR 564101
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
William E. Haver, A covering property for metric spaces, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 108–113. MR 0365504
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