# 4b: What is topological dimension?

## Description

This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by
others.

# 4b: 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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