Abstract
Let ϕX indicate the Freudenthal compactification of a rimcompact, completely regular Hausdorff spaceX. In this paper the spacesY which satisfyX⊑Y⊑ϕX are characterized. From this a characterization of whenX lies between its locally compact partL(X) and ϕ(L(X)) follows. Such spaces necessarily possess a compactification αX for whichCl αX (αX−X) is 0-dimensional. Conditions, including those internal toX, are provided which are necessary and sufficient for this property to hold.
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