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:• uasi-finite. exists a [L]-invertible mapping of a metrizable compactum X with e - dim X ⩽ [ L ] onto the Hilbert cube. y, we construct an example of a quasi-finite complex L such that its extension type [L] does not contain a finitely dominated complex.