Geodesic
Čech-Stone-like compactifications for general topological spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 159-163

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The problem whether every topological space $X$ has a compactification $Y$ such that every continuous mapping $f$ from $X$ into a compact space $Z$ has a continuous extension from $Y$ into $Z$ is answered in the negative. For some spaces $X$ such compactifications exist.
Classification : 18B30, 54B30, 54C20, 54D35
Keywords: compactification; mapping-extension 
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     author = {Hu\v{s}ek, Miroslav},
     title = {\v{C}ech-Stone-like compactifications for general topological spaces},
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Hušek, Miroslav. Čech-Stone-like compactifications for general topological spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 159-163. http://geodesic.mathdoc.fr/item/CMUC_1992__33_1_a17/