# Can any “relevant” topological spaces be decomposed into an uncountable product?

Can any "relevant", as meaning generally useful topological spaces be decomposed into an uncountable product of other topological spaces with the product topology?

• $X = X \times \prod_\mathbb{R} *$? – Najib Idrissi Jul 7 '14 at 8:00

Here, one considers the unit ball in $X'$ as a subset of
$$\prod_{x \in X} \overline{B}_{\Vert x \Vert}(0),$$
where the ball is formed in $\Bbb{K}$ (i.e. $\Bbb{R}$ or $\Bbb{C}$).