In mathematics, a topological algebra
is an algebra and at the same time a topological space, where the algebraic and the topological structures are coherent in a specified sense.
is a topological vector space together with a bilinear multiplication that turns
is called a "topological algebra with jointly continuous multiplication", and in the last, "with separately continuous multiplication".
The term was coined by David van Dantzig; it appears in the title of his doctoral dissertation (1931).