Geodesic
Wallman-type compaerifications and function lattices
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 4, pp. 679-683 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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Let $F \subset C^{\ast} (X)$ be a vector sublattice over $\mathbb{R}$ which separates points from closed sets of $X$. The compactification $e_{F}X$ obtained by embedding $X$ in a real cube via the diagonal map, is different, in general, from the Wallman compactification $\omega (Z(F))$. In this paper, it is shown that there exists a lattice $F_{z}$ containing $F$ such that $\omega (Z(F)) = \omega (Z(F_{z})) = e_{F}X$. In particular this implies that $\omega (Z(F)) \ge e_{F}X$. Conditions in order to be $\omega (Z(F)) = e_{F}X$ are given. Finally we prove that, if $\alpha X$ is a compactification of $X$ such that $Cl_{\alpha X} (\alpha X \setminus X)$ is $0$-dimensional, then there is an algebra $A \subset C^{ast} (X)$ such that $\omega (Z(A)) = e_{A} X = \alpha X$. 
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     author = {Caterino, Alessandro and Vipera, Maria Cristina},
     title = {Wallman-type compaerifications and function lattices},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
     pages = {679--683},
     year = {1988},
     volume = {Ser. 8, 82},
     number = {4},
     zbl = {0734.54016},
     mrnumber = {1139815},
     language = {en},
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}
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Caterino, Alessandro; Vipera, Maria Cristina. Wallman-type compaerifications and function lattices. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 4, pp. 679-683. http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_4_a7/

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