arXiv subjects

Hans Vermeer

Publications and source records attributed to Hans Vermeer.

3 recordsLinked to original sources

arXiv2024

$C$-embedding, Lindel\"ofness, and \v{C}ech-completeness

We show that in the class of Lindel\"of \v{C}ech-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, Lindel\"of and \v{C}ech-complete, are needed in the product result.

math.GN↗

arXiv2023

Some realcompact spaces

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 the space of natural numbers.

math.GN↗

arXiv2023

Closed copies of $\mathbb{N}$ in $\mathbb{R}^{\omega_1}$

We investigate closed copies of~$\mathbb{N}$ in powers of~$\mathbb{R}$ with respect to $C^*$- and $C$-embedding. We show that $\mathbb{R}^{\omega_1}$ contains closed copies of~$\mathbb{N}$ that are not $C^*$-embedded.

math.GN↗