Generalization of some properties of Banach algebras to fundamental locally multiplicative topological algebras

In this article we generalized some properties of Banach algebras, to a new class of topological algebras namely fundamental and fundamental locally multiplicative topological algebras (abbreviated by FLM). Also the new notion of sub-multiplicatively metrizable topological algebra is given and some well known spectral properties of Banach algebras are generalized to such kind of algebras.