| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4661425 | Topology and its Applications | 2007 | 12 Pages |
Abstract
Given a metric Peano continuum X we introduce and study the Hölder Dimension there is a -Hölder onto map of X as well as its topological counterpart is an admissible metric for X}. We show that for each convex metric continuum X the dimension Hö-dim(X) equals the fractal dimension of X. The topological Hölder dimension Hö-dim(Mn) of the n-dimensional universal Menger cube Mn equals n. On the other hand, there are 1-dimensional rim-finite Peano continua X with arbitrary prescribed Hö-dim(X)⩾1.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
