- Tytuł:
- Bing maps and finite-dimensional maps
- Autorzy:
- Levin, Michael
- Powiązania:
- https://bibliotekanauki.pl/articles/1205475.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
finite-dimensional maps
hereditarily indecomposable continua - Opis:
-
Let X and Y be compacta and let f:X → Y be a k-dimensional map. In [5] Pasynkov stated that if Y is finite-dimensional then there exists a map $g : X → \mathbb{I}^k$ such that dim (f × g) = 0. The problem that we deal with in this note is whether or not the restriction on the dimension of Y in the Pasynkov theorem can be omitted. This problem is still open.
Without assuming that Y is finite-dimensional Sternfeld [6] proved that there exists a map $g : X → \mathbb{I}^k$ such that dim (f × g) = 1. We improve this result of Sternfeld showing that there exists a map $g : X → mathbb{I}^{k+1}$ such that dim (f × g) =0. The last result is generalized to maps f with weakly infinite-dimensional fibers.
Our proofs are based on so-called Bing maps. A compactum is said to be a Bing compactum if its compact connected subsets are all hereditarily indecomposable, and a map is said to be a Bing map if all its fibers are Bing compacta. Bing maps on finite-dimensional compacta were constructed by Brown [2]. We construct Bing maps for arbitrary compacta. Namely, we prove that for a compactum X the set of all Bing maps from X to $\mathbb{I}$ is a dense $G_δ$-subset of $C(X, \mathbb{I})$. - Źródło:
-
Fundamenta Mathematicae; 1996, 151, 1; 47-52
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł