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 R^ω₁ 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.

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.