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Finite-dimensional maps and dendrites with dense sets of end points

Tom 106 / 2006

Colloquium Mathematicum 106 (2006), 83-91 MSC: Primary 54F45, 54B20; Secondary 55M10, 54F15, 54C65. DOI: 10.4064/cm106-1-7

Streszczenie

The first author has recently proved that if $f: X \to Y$ is a $k$-dimensional map between compacta and $Y$ is $p$-dimensional ($0 \le k,p < \infty$), then for each $0 \leq i \leq p+k$, the set of maps $g$ in the space $C(X,I^{p+2k+1-i})$ such that the diagonal product $f \times g:X \to Y\times I^{p+2k+1-i}$ is an $(i+1)$-to-$1$ map is a dense $G_{\delta }$-subset of $C(X,I^{p+2k+1-i})$. In this paper, we prove that if $f$ : $X \to Y$ is as above and $D_{j}$ $(j=1,\dots ,k)$ are superdendrites, then the set of maps $h$ in $C(X,\prod _{j=1}^{k}D_{j}\times I^{p+1-i})$ such that $f \times h:X \to Y\times (\prod _{j=1}^{k}D_{j}\times I^{p+1-i})$ is $(i+1)$-to-$1$ is a dense $G_{\delta }$-subset of $C(X,\prod _{j=1}^{k}D_{j}\times I^{p+1-i})$ for each $0\leq i \leq p$.

Autorzy

• Hisao KatoInstitute of Mathematics
University of Tsukuba
Ibaraki, 305-8571 Japan
e-mail
• Eiichi MatsuhashiInstitute of Mathematics
University of Tsukuba
Ibaraki, 305-8571 Japan
e-mail

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