JV
J. Vermeer
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1
We show that in the class of Lindelöf Čech-complete spaces the property of being C-embedded is quite well-behaved. It admits a useful characterization that can be used to show that products and perfect preimages of C-embedded spaces are again C-embedded. We also show that both properties, Lindelöf and Čech-complete, are needed in the product result.
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We show that in the class of Lindelöf Čech-complete spaces the property of being C-embedded is quite well-behaved. It admits a useful characterization that can be used to show that products and perfect preimages of C-embedded spaces are again C-embedded. We also show that both properties, Lindelöf and Čech-complete, are needed in the product result.
We investigate closed copies of N in powers of R with respect to C⁎- and C-embedding. We show that Rω1 contains closed copies of N that are not C⁎-embedded.
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We investigate closed copies of N in powers of R with respect to C⁎- and C-embedding. We show that Rω1 contains closed copies of N that are not C⁎-embedded.
We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of N.
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We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of N.
The authors, University of Kansas post-doctoral instructors at the time this note was written, exhibit an upper bound for the Lindelöf degree of a product space.
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The authors, University of Kansas post-doctoral instructors at the time this note was written, exhibit an upper bound for the Lindelöf degree of a product space.
The Ljusternik–Schnirelmann–Borsuk theorem for antipodal maps on the sphere can be stated as an intersection property of coverings of the sphere. We generalized this theorem to free finite-group actions on paracompact Hausdorff spaces and discuss how this result might be improved. We illustrate our results by a free action of the Klein four-group on the torus.
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The Ljusternik–Schnirelmann–Borsuk theorem for antipodal maps on the sphere can be stated as an intersection property of coverings of the sphere. We generalized this theorem to free finite-group actions on paracompact Hausdorff spaces and discuss how this result might be improved. We illustrate our results by a free action of the Klein four-group on the torus.