## Weakly infinite-dimensional compactifications and countable-dimensional compactifications.(English)Zbl 1212.54085

Summary: 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.

### MSC:

 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.) 54F45 Dimension theory in general topology
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