Definition:Vector Subspace/Proper Subspace
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Definition
Let $K$ be a division ring.
Let $\struct {S, +, \circ}_K$ be a $K$-algebraic structure with one operation.
Let $\struct {T, +_T, \circ_T}_K$ be a vector subspace of $\struct {S, +, \circ}_K$.
If $T$ is a proper subset of $S$, then $\struct {T, +_T, \circ_T}_K$ is a proper (vector) subspace of $\struct {S, +, \circ}_K$.
Sources
- 1990: John B. Conway: A Course in Functional Analysis (2nd ed.): $\S I.2$