Spaces having a weakly-infinite-dimensional compactification. (English) Zbl 0587.54055

The author introduces the property, small-weakly-infinite-dimensional (small-w.i.d.). He proves that for a separable metric space X, the following are equivalent, (1) X is small-w.i.d., (2) X has a small-w.i.d. completion, (3) X has a w.i.d. metric compactification.
He shows that every complete, separable metric, totally disconnected space is small-w.i.d. Since it is known that there exist complete, separable metric, totally disconnected spaces that are infinite dimensional but not countable dimensional, then the preceding shows that there exists a metric compactum which is neither countable dimensional nor strongly infinite dimensional. This is of course the result due to R. Pol [Proc. Am. Math. Soc. 82, 634-636 (1981; Zbl 0469.54014)].
Reviewer: L.Rubin


54F45 Dimension theory in general topology
55M10 Dimension theory in algebraic topology


Zbl 0469.54014
Full Text: DOI


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