Abstract
It is shown in this paper that for P = T 2 P = {T_2} or P = T 3 P = {T_3} every locally P P -closed space is a retract of a rim P P -closed, locally P P -closed space by an open, perfect retraction map. From this it follows that there exist noncompact, rim H H -closed, H H -closed spaces and noncompact, rim R R -closed, R R -closed spaces.
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