According to examples in dictionaries, "Up" is a preposition in the following sentences.
- He climbed up the steps
- They were climbing up a narrow mountain road.
- I ran up the stairs and saw Alison lying at the top.
To me, they look like prepositions, but they more look like adverbs. I don't know how to distinguish them. Why are they prepositions and not adverbs?
Thank you in advance.