Identify which of the following sets are open, which are closed, and which are neither. Find E°, , and ϑE and sketch E in each case.
a) E = {(x, y): x2 + 4y2 < 1}
b) E = {(x, y): x2 - 2x + y2 = 0}U {(x, 0) : x ∈ [2, 3]}
c) E = {(x, y) : y > x2, 0 < y < 1}
d) E = {(x, y): x2 - y2 < 1, -1 < y < 1}