# Category:Vector Subspaces

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This category contains results about **Vector Subspaces**.

Let $K$ be a division ring.

Let $\struct {S, +, \circ}_K$ be a $K$-algebraic structure with one operation.

Let $T$ be a closed subset of $S$.

Let $\struct {T, +_T, \circ_T}_K$ be a $K$-vector space where:

- $+_T$ is the restriction of $+$ to $T \times T$ and
- $\circ_T$ is the restriction of $\circ$ to $K \times T$.

Then $\struct {T, +_T, \circ_T}_K$ is a **(vector) subspace** of $\struct {S, +, \circ}_K$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Vector Subspaces"

The following 20 pages are in this category, out of 20 total.

### D

### I

### L

### S

- Set of Linear Subspaces is Closed under Intersection
- Set of Points for which Seminorm is Zero is Vector Subspace
- Subspace of Real Continuous Functions
- Subspace of Real Differentiable Functions
- Subspace of Real Functions of Differentiability Class
- Subspace of Riemann Integrable Functions
- Subspace of Smooth Real Functions