On two problems in extension theory

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable simplicial complex L the following conditions are equivalent:

•

L is quasi-finite.

•

There exists a L]-invertible mapping of a metrizable compactum X with e-dimX?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.