# A note on discrete $C$-embedded subspaces

In: Mathematica Slovaca, vol. 69, no. 2

## Details:

Year, pages: 2019, 469 - 473
Keywords:
$C$-embedded, realcompact spaces, $P_\lambda$-spaces, socle, isolated points, essential ideals
It is shown that in some non-discrete topological spaces, discrete subspaces with certain cardinality are $C$-embedded. In particular, this generalizes the well-known fact that every countable subset of $P$-spaces are $C$-embedded. In the presence of the measurable cardinals, we observe that if $X$ is a discrete space then every subspace of $υ X$ (i.e., the Hewitt realcompactification of $X$) whose cardinal is nonmeasurable, is a $C$-embedded, discrete realcompact subspace of $υ X$. This generalizes the well-known fact that the discrete spaces with nonmeasurable cardinal are realcompact.
Namdari, M., Siavoshi, M. 2019. A note on discrete $C$-embedded subspaces. In Mathematica Slovaca, vol. 69, no.2, pp. 469-473. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0239
Namdari, M., Siavoshi, M. (2019). A note on discrete $C$-embedded subspaces. Mathematica Slovaca, 69(2), 469-473. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0239