# Difference between revisions of "Addition theorem"

If a Hausdorff compactum $X$ can be represented as the union over a set of infinite cardinality $\leq\tau$ of its subspaces of weight $\leq\tau$, then the weight of $X$ does not exceed $\tau$. The addition theorem (which was formulated as a problem in [AlUr]) was established in [Sm] for $\tau=\aleph_0$ and in [Ar] in complete generality. Cf. Weight of a topological space.