  Let A be a topological space which is not finitely generated and CH(A) denote
the coreflective hull of A in Top. We construct a generator of the coreflective
subcategory SCH(A) consisting of all subspaces of spaces from CH(A) which is a
prime space and has the same cardinality as A. We also show that if A and B are
coreflective subcategories of Top such that the hereditary coreflective kernel
of each of them is the subcategory FG of all finitely generated spaces, then
the hereditary coreflective kernel of their join CH(A \cup B) is again FG.
