rc-convergence

Herrmann, Robert A.

doi:10.1090/S0002-9939-1979-0532157-5

rc-convergence
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Proc. Amer. Math. Soc. 75 (1979), 311-317 Request permission

Abstract:

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.

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