A topological partial algebra is a pair , where is a partial algebra and each of the operations is continuous in the product topology. Examples of topological partial algebras include topological groups, topological vector spaces, and topological fields. Specifically, a topological field is an example of a topological partial algebra that is not a topological algebra in the strict sense of the term.
Topological Partial Algebra
See also
Partial Algebra, Topological AlgebraThis entry contributed by Matt Insall (author's link)
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Insall, Matt. "Topological Partial Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TopologicalPartialAlgebra.html