Finite-to-one maps into Euclidean manifolds and spaces with disjoint disks properties |
| |
Authors: | Alex Karassev Murat Tuncali |
| |
Affiliation: | Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, PO Box 5002, North Bay, ON, P1B 8L7, Canada |
| |
Abstract: | It is shown that every Euclidean manifold M has the following property for any m?1: If f:X→Y is a perfect surjection between finite-dimensional metric spaces, then the mapping space C(X,M) with the source limitation topology contains a dense Gδ-subset of maps g such that dimBm(g)?mdimf+dimY−(m−1)dimM. Here, Bm(g)={(y,z)∈Y×M||f−1(y)∩g−1(z)|?m}. The existence of residual sets of finite-to-one maps into product of manifolds and spaces having disjoint disks properties is also obtained. |
| |
Keywords: | primary, 54F45 secondary, 55M10 |
本文献已被 ScienceDirect 等数据库收录! |
|