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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

rc-convergence


Author: Robert A. Herrmann
Journal: Proc. Amer. Math. Soc. 75 (1979), 311-317
MSC: Primary 54D25; Secondary 54A99
MathSciNet review: 532157
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0532157-5
PII: S 0002-9939(1979)0532157-5
Keywords: S-closed, extremally disconnected, convergence structure, nearly-compact, quasi-H-closed, almost-regular, Fomin extension, weakly-$ {T_2}$, projective objects
Article copyright: © Copyright 1979 American Mathematical Society