Topological algebra
In mathematics, a topological algebra A {\displaystyle A} is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense. == Definition == A topological algebra A {\displaystyle A} over a topological field K {\displaystyle K} is a topological vector space together with a bilinear multiplication ⋅ : A × A → A {\displaystyle \cdot :A\times A\to A} , ( a , b ) ↦ a ⋅ b {\displaystyle (a,b)\mapsto a\cdot b} that turns A {\displaystyle A} into an algebra over K {\displaystyle K} and is continuous in some definite sense.