Pairs of Topological Algebras
Mati Abel, Mati Abel · Rocky Mountain Journal of Mathematics · 2007
Let (A, B) be a pair of topological algebras A and B. Conditions for A, respectively B, to be a Gelfand-Mazur algebra or an exponentially galbed algebra, if B, respectively A, is one, are given.It is shown that hom A, the set of all nonzero continuous homomorphisms from A onto K endowed with Gelfand topology, and hom B are homeomorphic if either hom A is equicontinuous or hom B is locally equicontinuous.Topological algebras A with jointly continuous multiplication for which a) the completion à is a Gelfand-Mazur algebra or exponentially galbed algebra or b) hom A and hom à are homeomorphic are described.