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

• Autorzy: Hisao Kato , Eiichi Matsuhashi
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 54F15: Continua and generalizations
• 55M10: Dimension theory
• 54B20: Hyperspaces
• 54C65: Selections
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2006
• Tom: 106
• Numer: 1
• Strony: 83-91

Daty

wydano

2006

Twórcy

autor

Hisao Kato

• Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan

autor

Eiichi Matsuhashi

• Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan

Identyfikatory

DOI

10.4064/cm106-1-7