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

Borst, Piet

Topology Appl. 21, 261-268 (1985).

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

MSC:

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

Keywords:

metric compactification; small-weakly-infinite-dimensional space

Citations:

Zbl 0469.54014

References:

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