Restorability of the Vietoris topology according to the compacts in the space of closed subgroups

• Date: 1990
• Main Authors: Piskunov, A. G., Пискунов, А. Г.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 1990
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8838
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

It is proved that the space of closed subgroups ${\mathfrak L} (G)$ of a locally compact $\sigma$-compact group $G$ is a $k$-space if and only if each noncompact subgroup of $G$ can be represented as the intersection of a countable number of open sets.