Geodesic
Weakly infinite-dimensional compactifications and countable-dimensional compactifications
Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 147-154.

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In this paper we give a characterization of a separable metrizable space having a metrizable S-weakly infinite-dimensional compactification in terms of a special metric. Moreover, we give two characterizations of a separable metrizable space having a metrizable countable-dimensional compactification.
Classification : 54D35, 54F45
Keywords: S-weakly infinite-dimensional; countable-dimensional; compactification 
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Kimura, Takashi; Komoda, Chieko. Weakly infinite-dimensional compactifications and countable-dimensional compactifications. Commentationes Mathematicae Universitatis Carolinae, Tome 49 (2008) no. 1, pp. 147-154. http://geodesic.mathdoc.fr/item/CMUC_2008__49_1_a13/