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


Locally $ P$-closed spaces and rim $ P$-closed spaces

Author: Dix H. Pettey
Journal: Proc. Amer. Math. Soc. 87 (1983), 543-548
MSC: Primary 54D25; Secondary 54C15
MathSciNet review: 684655
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Abstract: It is shown in this paper that for $ P = {T_2}$ or $ P = {T_3}$ every locally $ P$-closed space is a retract of a rim $ P$-closed, locally $ P$-closed space by an open, perfect retraction map. From this it follows that there exist noncompact, rim $ H$-closed, $ H$-closed spaces and noncompact, rim $ R$-closed, $ R$-closed spaces.

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PII: S 0002-9939(1983)0684655-2
Keywords: $ P$-closed space, locally $ P$-closed space, rim $ P$-closed space
Article copyright: © Copyright 1983 American Mathematical Society