On subsequential spaces

AbstractSimple generators for the coreflective category of subsequential spaces, one of them countable, are constructed. Every such must have subsequential order ω1. Subsequentialness is a local property and a countable property, both in a strong sense. A T2-subsequential space may be pseudocompact without being sequential, in contrast to T2-subsequential compact (countably compact, sequentially compact) spaces all being sequential. A compact subsequential space need not be sequential