On finite-dimensional maps and other maps with "small" fibers
Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 127-133
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We prove that if f is a $k$-dimensional map on a compact metrizable space $X$ then there exists a σ-compact $(k-1)$-dimensional subset $A$ of $X$ such that $f|X∖A$ is 1-dimensional. Equivalently, there exists a map $g$ of $X$ in $I^k$ such that $\dim(f × g)=1$. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that $f(X)$ is finite-dimensional. These results are then extended to maps with fibers restricted to some classes of spaces other than the class of $k$-dimensional spaces. For example: if f has weakly infinite-dimensional fibers then $\dim(f|X∖A) ≤ 1$ for some σ-compact weakly infinite-dimensional subset $A$ of $X$. The proof applies essentially the properties of hereditarily indecomposable continua.
@article{10_4064_fm_147_2_127_133,
author = {Yaki Sternfeld},
title = {On finite-dimensional maps and other maps with "small" fibers},
journal = {Fundamenta Mathematicae},
pages = {127--133},
publisher = {mathdoc},
volume = {147},
number = {2},
year = {1995},
doi = {10.4064/fm-147-2-127-133},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-147-2-127-133/}
}
TY - JOUR AU - Yaki Sternfeld TI - On finite-dimensional maps and other maps with "small" fibers JO - Fundamenta Mathematicae PY - 1995 SP - 127 EP - 133 VL - 147 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/fm-147-2-127-133/ DO - 10.4064/fm-147-2-127-133 LA - en ID - 10_4064_fm_147_2_127_133 ER -
Yaki Sternfeld. On finite-dimensional maps and other maps with "small" fibers. Fundamenta Mathematicae, Tome 147 (1995) no. 2, pp. 127-133. doi: 10.4064/fm-147-2-127-133
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