Definition of up preposition from the Oxford Advanced American Dictionary

     

    up

     preposition
    preposition
    NAmE//ʌp//
     
     
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  1. 1to or in a higher position somewhere She climbed up the flight of steps. The village is further up the valley.
  2. 2along or further along a road or street We live just up the road, past the post office.
  3. 3 toward the place where a river starts a cruise up the Hudson
  4. Idioms
    up and down something
     
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    in one direction and then in the opposite direction along something I looked up and down the corridor.
See the Oxford Advanced Learner's Dictionary entry: up