Minimal sequential Hausdorff spaces

A sequential space (X,T) is called minimal sequential if no sequential topology on X is strictly weaker than T . This paper begins the study of minimal sequential Hausdorff spaces. Characterizations ofminimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of spaces, for example, minimal Hausdorff spaces, countably compact spaces, H-closed spaces, SQ-closed spaces, and subspaces of minimal sequential spaces, are investigated. While the property of being sequential is not (in general) preserved by products, some information is provided on the question of when the product of minimal sequential spaces is minimal sequential.