ON CONTINUITY OF A-LINEAR MAPS

While I was working on generalization of Serre-Swan-Mallios Theorem which gives us a ”bridge” between algebraic K-theory and topological K-theory, it became necessary to establish the continuity of all A-linear maps between finitely generated projective A-modules, where A is an (topological) algebra. This problem was reduced to the following problem: under which conditions on topological algebra A all A-linear maps f : A^{n} → A^{m} are continuous for every n, m ∈ ℕ? For unital algebra A the positive answer was known for long time already. In this talk we will introduce a class of (nonunital) topological algebras for which the answer is still positive.