Let $V$ denote a vector space (or any other kind of algebraic structure).
Question. Letting $I$ denote a fixed set and $X$ denote an $I$-indexed family of subspaces (subalgebras) of $V$, is there better notation than $\bigoplus_{i:I} X_i = \sum_{i:I}X_i$ and/or $\bigsqcup_{i:I} X_i = \bigvee_{i:I}X_i$ to mean that the projection $\bigsqcup_{i:I} X_i \twoheadrightarrow \bigvee_{i:I}X_i$ is injective?
Also: is there accepted terminology for this condition?
For example, if $A$ denotes an $n \times n$ real matrix and $X : \mathrm{Eigenvalue}(A) \rightarrow \mathrm{Subspace}(\mathbb{R}^n)$ is the corresponding eigenspace function, then I'd like to be able to say: "$X$ satisfies [whatever]."