Category:Topological Vector Spaces

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This category contains results about Topological Vector Spaces.
Definitions specific to this category can be found in Definitions/Topological Vector Spaces.

Let $\struct {K, +_K, \circ_K, \tau_K}$ be a topological field.

Let $\struct {X, +_X, \circ_X, \tau_X}$ be a vector space over $K$.

Let $\tau_X \times \tau_X$ be the product topology of $\tau_X$ and $\tau_X$.

Let $\tau_K \times \tau_X$ be the product topology of $\tau_K$ and $\tau_X$.

We say that $\struct {X, \tau_X}$ is called a topological vector space if and only if:

\((1)\)   $:$   $+_X: \struct {X \times X, \tau_X \times \tau_X} \to \struct {X, \tau_X}$ is continuous      
\((2)\)   $:$   $\circ_X : \struct {K \times X, \tau_K \times \tau_X} \to \struct {X, \tau_X}$ is continuous      


This category has the following 23 subcategories, out of 23 total.

Pages in category "Topological Vector Spaces"

The following 67 pages are in this category, out of 67 total.