rc-convergence

The re-convergence structure is introduced and used to characterize S-closed spaces in terms of regular-closed (re) or regular-open sets. S-closed spaces are compared with nearly-compact, quasi-H-closed spaces and compact semiregularizations. Weakly-${T_2}$ extremally disconnected spaces are embedded into the Fomin S-closed extension. For any discrete space, $\beta (X)$ is shown to be S-closed and the category of nearly-compact Hausdorff spaces and $\theta$-continuous mappings has the S-closed spaces as its protective objects. An explicit example of a noncompact Hausdorff S-closed space is constructed. Finally, various mappings which preserve S-closedness are investigated.