F-space

In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d : V × V → R so that

Some authors call these spaces Fréchet spaces, but usually the term is reserved for locally convex F-spaces. The metric may or may not necessarily be part of the structure on an F-space; many authors only require that such a space be metrizable in a manner that satisfies the above properties.