arXiv subjects
Publications and source records attributed to A. V. Karasev.
We present results on simplifying an acting group preserving properties of actions: transitivity, being a coset space and preserving a fixed equiuniformity in case of a $G$-Tychonoff space.
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.
Some properties of [L]-homotopy group for finite complex L are investigated. It is proved that for complex L whose extension type lying between Sn and Sn+1 n-th [L]-homotopy group of Sn is isomorphic to Z.
The paper is devoted to generalization of well-known Michael's Selection theorem on the case of extension dimension.