Category:Weak Topologies on Topological Vector Spaces
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This category contains results about Weak Topologies on Topological Vector Spaces.
Definitions specific to this category can be found in Definitions/Weak Topologies on Topological Vector Spaces.
Let $K$ be a topological field.
Let $X$ be a topological vector space over $K$.
Let $X^\ast$ be the topological dual space of $X$.
Let $w$ be the initial topology on $X$ with respect to $X^\ast$.
We say that $w$ is the weak topology on $X$ if and only if:
- for each $x \in X \setminus \set {\mathbf 0_X}$ there exists $f \in X^\ast$ such that $\map f x \ne 0$.
That is, if and only if $w$ "separates the points of $X$".
Subcategories
This category has the following 6 subcategories, out of 6 total.
Pages in category "Weak Topologies on Topological Vector Spaces"
The following 19 pages are in this category, out of 19 total.