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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

3 votes
1 answer
928 views

Specific criterion for the sum of two closed sets to be closed

Let $Y$ and $Z$ be two closed subspaces of a Banach space $X$ with $Y\cap Z=\{0\}$. I know that $Y+Z$ is a closed subspace of $X$ $\iff \exists \alpha > 0:\quad \lVert y\rVert \le \alpha\lVert y+z\rVe …
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