On two problems in extension theory
Abstract
Description
In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent:
(i) L is quasi-finite. (ii) There exists a [L]-invertible mapping of a metrizable compactum X with e-dim X = [L] onto the Hilbert cube.
Finally, we construct an example of a quasi-finite complex L such that its extension type [L] does not contain a finitely dominated complex.