lotus



previous page: 07 What is fractal dimension? How is it calculated?
  
page up: sci.fractals FAQ
  
next page: 09 What is a strange attractor?

08 What is topological dimension?




Description

This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

08 What is topological dimension?

Topological dimension is the "normal" idea of dimension; a
point has topological dimension 0, a line has topological dimension 1,
a surface has topological dimension 2, etc.

For a rigorous definition:
A set has topological dimension 0 if every point has arbitrarily small
neighborhoods whose boundaries do not intersect the set.

A set S has topological dimension k if each point in S has arbitrarily
small neighborhoods whose boundaries meet S in a set of dimension k-1,
and k is the least nonnegative integer for which this holds.

 

Continue to:













TOP
previous page: 07 What is fractal dimension? How is it calculated?
  
page up: sci.fractals FAQ
  
next page: 09 What is a strange attractor?