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Category of topological vector spaces
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the category of topological vector spaces is the <a href="/facts/Category_(category_theory)/7WzxUThf">category</a> whose <a href="/facts/Object_(category_theory)/7WzxUThf">objects</a> are <a href="/facts/Topological_vector_space/XRex1ChN">topological vector spaces</a> and whose <a href="/facts/Morphism/Kdpuyz3S">morphisms</a> are <a href="/facts/Continuous_linear_map/KcqjDBrJ">continuous linear maps</a> between them. This is a category because the <a href="/facts/Function_composition/r5Pvnmth">composition</a> of two continuous linear maps is again a continuous linear map. The category is often denoted TVect or TVS. </p><p>Fixing a <a href="/facts/Topological_field/qxQqzhCy">topological field</a> <i>K</i>, one can also consider the <a href="/facts/Subcategory/k4lEeDDb">subcategory</a> TVect<i>K</i> of topological vector spaces over <i>K</i> with continuous <i>K</i>-linear maps as the morphisms. </p>