ski ĭ , ▁William ▁C . ▁Water house ▁and ▁K . ▁Braun er ▁showed ▁that ▁this ▁result ▁can ▁be ▁extended ▁to ▁the ▁class ▁of ▁all ▁quasi - complete ▁bar re led ▁spaces ▁( in ▁particular , ▁to ▁all ▁Fr éch et ▁spaces ). ▁In ▁the ▁ 1 9 9 0 s ▁Serge i ▁Ak bar ov ▁gave ▁a ▁description ▁of ▁the ▁class ▁of ▁the ▁topological ▁vector ▁spaces ▁that ▁satisfy ▁a ▁stronger ▁property ▁than ▁the ▁classical ▁Pon try agin ▁ref lex ivity , ▁namely , ▁the ▁identity ▁▁ ▁where ▁ ▁means ▁the ▁space ▁of ▁all ▁linear ▁continuous ▁function als ▁ ▁end owed ▁with ▁the ▁topology ▁of ▁uniform ▁convergence ▁on ▁totally ▁bounded ▁sets ▁in ▁ ▁( and ▁ ▁means ▁the ▁dual ▁to ▁ ▁in ▁the ▁same ▁sense ). ▁The ▁spaces ▁of ▁this ▁class ▁are ▁called ▁s tere ot ype ▁spaces , ▁and ▁the ▁corresponding ▁theory ▁found ▁a ▁series ▁of ▁applications ▁in ▁Function al ▁analysis ▁and ▁Ge ometry , ▁including ▁the ▁general ization ▁of ▁Pon try agin ▁du ality ▁for ▁non - comm ut ative ▁topological ▁groups . ▁ ▁D ual ities ▁for ▁non - comm ut ative ▁topological ▁groups ▁For ▁non - comm ut ative ▁locally ▁compact ▁groups ▁ ▁the ▁classical ▁Pon try agin ▁construction ▁stops ▁working ▁for ▁various ▁reasons , ▁in ▁particular , ▁because ▁the ▁characters ▁don ' t ▁always ▁separate ▁the ▁points ▁of ▁, ▁and ▁the ▁ir reducible ▁representations ▁of ▁ ▁are ▁not ▁always ▁one - dimensional . ▁At ▁the ▁same ▁time ▁it ▁is ▁not ▁clear ▁how ▁to ▁introduce ▁multiplication ▁on ▁the ▁set