In functional analysis, an F-space is a vector space X {\displaystyle X} over the real or complex numbers together with a metric d : X × X → R {\displaystyle d:X\times X\to \mathbb {R} } such that Scalar multiplication in X {\displaystyle X} is continuous with respect to d {\displaystyle d} and the standard metric on R {\displaystyle \mathbb {R} } or C. Wikipedia