A closed ideal is a specific type of ideal in a topological algebra that is also a closed set with respect to the topology of that algebra. This means it not only adheres to the algebraic properties of being an ideal, such as being a subspace closed under addition and scalar multiplication, but it also fulfills the topological condition of being closed, ensuring limits of convergent sequences from the ideal remain within it. Understanding closed ideals helps in analyzing the structure and properties of topological algebras.
congrats on reading the definition of closed ideal. now let's actually learn it.