In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space X {\displaystyle X} in which every sequence in its continuous dual space X ′ {\displaystyle X^{\prime }} that converges in the weak-* topology σ {\displaystyle \sigma \left} will also converge when X ′ {\displaystyle X^{\prime }} is endowed with σ, {\displaystyle \sigma \left,} which is the weak topology induced on X ′ {\displaystyle X^{\prime }} by its bidual. Wikipedia