How do you call the space $\mathbb{Q}^{\mathbb{N}}$?

Question

How do you call the space $\mathbb{Q}^{\mathbb{N}}$?

I also know it under the name $\mathbb{Q}^{\omega}$.

Topologically, $\mathbb{N}$ and $\omega$ are the same thing basically, denoting the countable product of rationals.

However, I am asking for other names, since I completely fail to google anything about $\mathbb{Q}^{\mathbb{N}}$, the best I can find is $\mathbb{Q}^{\mathbb{n}}$, which is something different.

How do you search for the stuff about $\mathbb{Q}^{\mathbb{N}}$? Does it have any special name?

Thank you.

Answer 1

The space is just the space of all rational sequences since its the set of all functions from the naturals to the rationals.