Let E be a Jordan region in Rn. a) Prove that E and are Jordan regions.

Question:

Let E be a Jordan region in Rn.
a) Prove that E° and are Jordan regions.
b) Prove that Vol(Eo) = Vol() = Vol(E).
c) Prove that Vol(E) > 0 if and only if E° ≠ 0.
d) Let f: [a, b] → R be continuous on [a, b]. Prove that the graph of y = f(x), x ∈ [a, b], is a Jordan region in R2.
e) Does part d) hold if continuous is replaced by integrablel How about bounded?