boundary vs extremity

boundary and extremity both are nouns.

Word	Noun	Adjective	Verb	Adverb
boundary	Yes	No	No	No
extremity	Yes	No	No	No

As nouns, extremity is a hypernym of boundary; that is, extremity is a word with a broader meaning than boundary:

boundary (noun)	extremity (noun)
the greatest possible degree of something	an external body part that projects from the body
the line or plane indicating the limit or extent of something	that part of a limb that is farthest from the torso
a line determining the limits of an area	the outermost or farthest region or point
	the greatest or utmost degree
	an extreme condition or state (especially of adversity or disease)