On subsequential spaces (Q756183)

A subset A of a space is called sequentially closed iff no sequence in A converges to a point outside of A. A space is called sequential [first author, Fundam. Math. 57, 107-115 (1965; Zbl 0132.178)] iff each of its sequentially closed sets is closed and is called subsequential iff it is a subspace of some sequential space. The paper under review both collects certain known results about subsequential spaces (sometimes with new proofs) and provides many new and interesting results about such spaces. Among the new results are the following: The full subcategory of subsequential spaces is a (mono) coreflective subcategory of Top, and is simply generated by a countable space. However, it has no compact generator (unlike the subcategory of sequential spaces) nor any generator with subsequential order less than \(\omega_ 1\). There are compact subsequential spaces as well as Hausdorff pseudocompact zero-dimensional subsequential spaces that are not sequential.