Abstract
LetX be a locally compact non compact space. Necessary and sufficient conditions forfX/X to be a retract offX are given wherefX is the Freudenthal compactification ofX. LetX be a locally compact and zero dimensional space,m be any cardinal number andJ be a set with cardinalitym. It is proved thatX has a dyadic family of powerm if and only if there exist and compactificationY ofX such thatY/X=2J andY/X is a retract ofY.
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Ünlü, Y., Kuyucu, F. Compactifications whose remainders are zero dimensional and retract. Rend. Circ. Mat. Palermo 45, 201–210 (1996). https://doi.org/10.1007/BF02844486
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DOI: https://doi.org/10.1007/BF02844486