run up vs hem

run up is not a noun while hem is a noun.

Word	Noun	Adjective	Verb	Adverb
run up	No	No	Yes	No
hem	Yes	No	Yes	No

As verbs, hem is a hyponym of run up; that is, hem is a word with a more specific, narrower meaning than run up:

run up (noun)	hem (noun)
	the edge of a piece of cloth; especially the finished edge that has been doubled under and stitched down
	the utterance of a sound similar to clearing the throat; intended to get attention, express hesitancy, fill a pause, hide embarrassment, warn a friend, etc.

run up (verb)	hem (verb)
pile up (debts or scores)	utter `hem' or `ahem'
raise by using ropes and pulleys	fold over and sew together to provide with a hem
fasten by sewing; do needlework
make by sewing together quickly
accumulate, sometimes as a debt