# What is the TOPOLOGICAL DIMENSION of?

1. Jul 10, 2008

### Take_it_Easy

Let $${\mathbb I} = {\mathbb R} \setminus {\mathbb Q}$$ the set of the irrational numbers of the real line.

What is the topological dimension of
$${\mathbb R}^2 \setminus {\mathbb I} \times {\mathbb I}$$ ????

2. Jul 11, 2008

### Take_it_Easy

Just discovered, by myself, that it is 1 .

:tongue:

I just hope that someone can enjoy this result as I do!

Last edited: Jul 11, 2008
3. Jul 11, 2008

### net_nubie

Could you explain what is topological dimension please?

4. Jul 11, 2008

### ice109

apparently

We say a topological space X has topological dimension m if every covering C of X has a refinementC' in which every point of X occurs in at most m+1 sets in C' , and m is the smallest such integer. Actually, this version of the definition of dimension (called the covering dimension) makes the most sense for compact spaces X.