Hereditarily aspherical compacta
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- by Jerzy Dydak and Katsuya Yokoi PDF
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Abstract:
The notion of (strongly) hereditarily aspherical compacta introduced by Daverman (1991) is modified. The main results are:
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If $X\in LC^{1}$ is a hereditarily aspherical compactum, then $X\in$ ANR. In particular, $X$ is strongly hereditarily aspherical.
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Suppose $f:X\to Y$ is a cell-like map of compacta and $f^{-1}(A)$ is shape aspherical for each closed subset $A$ of $Y$. Then
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$Y$ is hereditarily shape aspherical,
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$f$ is a hereditary shape equivalence,
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$\dim X\ge \dim Y$.
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Suppose $G$ is a group containing integers. Then the following conditions are equivalent:
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$\dim X\le 2$ and $\dim _{G}X=1$,
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$\dim _{G*_{\mathbf {Z}}G}X=1$.
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Suppose $G$ is a group containing integers. If $\dim X\le 2$ and $\dim _{G}X=1$, then $X$ is hereditarily shape aspherical.
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Let $X$ be a two-dimensional, locally connected and semilocally simply connected compactum. Then, for any compactum $Y$ \begin{equation*}\dim (X \times Y) = \dim X + \dim Y.\end{equation*}
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Additional Information
- Jerzy Dydak
- Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
- Email: dydak@math.utk.edu
- Katsuya Yokoi
- Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba-shi, Ibaraki, 305, Japan
- Email: yokoi@sakura.cc.tsukuba.ac.jp
- Received by editor(s): April 6, 1994
- Received by editor(s) in revised form: November 19, 1994
- Communicated by: James West
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1933-1940
- MSC (1991): Primary 55M10, 54F45
- DOI: https://doi.org/10.1090/S0002-9939-96-03221-2
- MathSciNet review: 1307513