In this note we study algebra seminorms on a functions algebra and we relate the existence of algebra norms on with the topology of . Also a theorem, that states which are the continuous characters, is demonstrated in a class of seminormed algebras.
Let be a metric space and . We study homological properties and different types of amenability of Lipschitz algebras and their second duals. Precisely, we first provide some basic properties of Lipschitz algebras, which are important for metric geometry to know how metric properties are reflected in simple properties of Lipschitz functions. Then we show that all of these properties are equivalent to either uniform discreteness or finiteness of . Finally, some results concerning the character...