▁ ▁Sm ooth ▁manif olds ▁are ▁sometimes ▁defined ▁as ▁embedded ▁sub man if olds ▁of ▁real ▁coordinate ▁space ▁R n , ▁for ▁some ▁n . ▁This ▁point ▁of ▁view ▁is ▁equivalent ▁to ▁the ▁usual , ▁abstract ▁approach , ▁because , ▁by ▁the ▁Whit ney ▁embedding ▁theorem , ▁any ▁second - count able ▁smooth ▁( abstract ) ▁m - man if old ▁can ▁be ▁smooth ly ▁embedded ▁in ▁R 2 m . ▁ ▁Notes ▁ ▁References ▁▁▁ ▁Category : D iffer ential ▁topology ▁Category : Man if olds <0x0A> </s> ▁Hung ▁Li ang - ch uan ▁or ▁U ya ▁P aw an ▁() ▁is ▁a ▁politician ▁in ▁the ▁Republic ▁of ▁China . ▁He ▁served ▁as ▁the ▁Deput y ▁Minister ▁of ▁the ▁Council ▁of ▁Ind igen ous ▁Pe op les ▁of ▁the ▁Executive ▁Y uan ▁starting ▁in ▁May ▁ 2 0 1 2 . ▁ ▁Early ▁political ▁life ▁Prior ▁to ▁his ▁appointment ▁as ▁Deput y ▁Minister ▁of ▁the ▁Council ▁of ▁Ind igen ous ▁Pe op les , ▁Hung ▁was ▁the ▁director ▁of ▁the ▁Department ▁of ▁Econom ic ▁and ▁Public ▁Const ruction ▁of ▁the ▁same ▁council . ▁ ▁See ▁also ▁ ▁Taiwan ese ▁ab orig ines ▁ ▁References ▁ ▁Category : Pol it ical ▁office - hold ers ▁in ▁the ▁Republic ▁of ▁China ▁on ▁Taiwan ▁Category : L iving ▁people ▁Category : Year ▁of ▁birth ▁missing ▁( l iving ▁people ) <0x0A> </s> ▁Fri ar ▁Gate ▁Bridge , ▁also ▁known ▁as ▁Hand ys ide ▁Bridge ▁after ▁the ▁company ▁that ▁built ▁it , ▁is ▁a ▁railway ▁bridge