Two examples on preimages of metric spaces
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- by N. Noble PDF
- Proc. Amer. Math. Soc. 36 (1972), 586-590 Request permission
Abstract:
Examples are given to show that the product of a compact ${T_1}$-space with a metric space need not be a k-space, and that the product of a countably compact Hausdorff space with a metric space need not be a quasi-k-space. These examples show that the separation assumptions cannot be omitted in the following two known results: Each Hausdorff perfect preimage of a k-space is a k-space. Each regular quasi-perfect preimage of a ${T_1}$ quasi-k-space is a quasi-k-space. Some related results, perhaps of independent interest, are also obtained.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 586-590
- MSC: Primary 54D50
- DOI: https://doi.org/10.1090/S0002-9939-1972-0310840-8
- MathSciNet review: 0310840