Locally 𝑃-closed spaces and rim 𝑃-closed spaces

Pettey, Dix H.

doi:10.1090/S0002-9939-1983-0684655-2

Locally $P$-closed spaces and rim $P$-closed spaces
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by Dix H. Pettey

Proc. Amer. Math. Soc. 87 (1983), 543-548

DOI: https://doi.org/10.1090/S0002-9939-1983-0684655-2

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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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