A generating family for the Freudenthal compactification of a class of rimcompact spaces

Tom 178 / 2003

Jesús M. Domínguez Fundamenta Mathematicae 178 (2003), 203-215 MSC: 54D35, 54C40. DOI: 10.4064/fm178-3-2


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 $\gamma X$ 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 $\gamma X$ is the Freudenthal compactification of $X$. For $X$ Hausdorff and locally compact, we establish an isomorphism between the lattice of all subalgebras of $F(X)/C_{\rm K}(X)$ and the lattice of all compactifications of $X$ with zero-dimensional remainder, the finite-dimensional subalgebras corresponding to the compactifications with finite remainder.


  • Jesús M. DomínguezDepartamento de Álgebra, Geometría y Topología
    Facultad de Ciencias
    Universidad de Valladolid
    47005 Valladolid, Spain

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