Definition of up preposition from the Oxford Advanced Learner's Dictionary

      

    up

     preposition
    preposition
    BrE BrE//ʌp//
     
    ; NAmE NAmE//ʌp//
     
     
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  1. 1  to or in a higher position somewhere She climbed up the flight of steps. The village is further up the valley.
  2. 2  along or further along a road or street We live just up the road, past the post office.
  3. 3  towards the place where a river starts a cruise up the Rhine
  4. Word Origin Old English up(p), uppe, of Germanic origin; related to Dutch op and German auf.Idioms in one direction and then in the opposite direction along something I looked up and down the corridor. (taboo, slang) an offensive way of being rude to somebody, for example because they have said something that makes you angry
See the Oxford Advanced American Dictionary entry: up