## Tsukuba Journal of Mathematics

### A characterization of compacta which admit acyclic $UV^{n-1}$ -resolutions

Akira Koyama

#### Abstract

Let $R$ be a commutative ring with identity. The main result of the paper is the following: THEOREM. Let $f:Z\rightarrow X$ be a $UV^{n-1}$-mapping from a compactum $Z$ of dimension $\leq n$ onto a compactum $X$. If $H^{n}(f^{-1}(x);R)=0$ for all $x\in X$, then $a-dim_{R}X\leq n$. As its consequence, we have a characterization of compacta $X$ of $a-dim_{R}X\leq n$. THEOREM. A compactum $X$ admits a $UV^{n-1}$ -mapping $f:Z\rightarrow X$ from a compactum $Z$ of dimension $\leq n$ onto $X$ such that $H^{n}(f^{-1}(x);R)=0$ for all $x\in X$ if and only if $a-dim_{R}X\leq n$.

#### Article information

Source
Tsukuba J. Math., Volume 20, Number 1 (1996), 115-121.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496162982

Digital Object Identifier
doi:10.21099/tkbjm/1496162982

Mathematical Reviews number (MathSciNet)
MR1406033

Zentralblatt MATH identifier
0888.54033

#### Citation

Koyama, Akira. A characterization of compacta which admit acyclic $UV^{n-1}$ -resolutions. Tsukuba J. Math. 20 (1996), no. 1, 115--121. doi:10.21099/tkbjm/1496162982. https://projecteuclid.org/euclid.tkbjm/1496162982