A generating family for the Freudenthal compactification of a class of rimcompact spaces
Fundamenta Mathematicae, Tome 178 (2003) no. 3, p. 203.

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For X a Tikhonov space, let F(X) be the algebra of all real-valued continuous functions on X that assume only finitely many values outside some compact subset. We show that F(X) generates a compactification γX of X if and only if X has a base of open sets whose boundaries have compact neighborhoods, and we note that if this happens then γX is the Freudenthal compactification of X. For X Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of F ( X ) / C K ( X ) and the lattice of all compactifications of X with zero-dimensional remainder, the finite-dimensional subalgebras corresponding to the compactifications with finite remainder.
Classification : 54D35, 54C40
Mots-clés : compactification, rimcompact, ring of continuous functions, function algebra, Boolean ring, maximal ideal, idempotent, zero-dimensional 
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     title = {A generating family for the {Freudenthal} compactification of a class of rimcompact spaces},
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Jesús M. Domínguez. A generating family for the Freudenthal compactification of a class of rimcompact spaces. Fundamenta Mathematicae, Tome 178 (2003) no. 3, p. 203. https://geodesic-test.mathdoc.fr/item/FUNDAM_2003__178_3_282914/