We study the heredity of the classes of generalized metric spaces (for example, spaces with a \(\sigma\)-hereditarily closure-preserving \(k\)-network, spaces with a point-countable base, spaces with a base of countable order, spaces with a point-regular base, Nagata-spaces, \(c\)-semi-stratifiable spaces, \(\gamma\)-spaces, semi-metrizable spaces)...

Some generalized metric properties on hyperspaces with the Vietoris topology