Cell-like resolutions preserving cohomological dimensions

We prove that for every compactum $X$ with ${dim}_{ℤ} X \leq n \geq 2$ there is a cell-like resolution $r : Z \to X$ from a compactum $Z$ onto $X$ such that $dim Z \leq n$ and for every integer $k$ and every abelian group $G$ such that ${dim}_{G} X \leq k \geq 2$ we have ${dim}_{G} Z \leq k$ . The latter property implies that for every simply connected CW–complex $K$ such that $e-edim X \leq K$ we also have $e-dim Z \leq K$ .

Keywords

Cohomological dimension, cell-like resolution

Mathematical Subject Classification 2000

Primary: 55M10, 54F45

References

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Publication

Received: 7 April 2003

Revised: 1 December 2003

Accepted: 9 December 2003

Published: 31 December 2003

Authors

Michael Levin
Department of Mathematics Ben Gurion University of the Negev P.O.B. 653 Be’er Sheva 84105 ISRAEL

Volume 3, issue 2 (2003)

Michael Levin