# 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.

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