Question

is Compact circle or not ​

Answer 1

COMPACT

then f is continuous, and the unit circle is f([0,2π]) and so it's a compact set of R2 as image of the compact [0,2π] by the continuous function f.

Answer 2

then f is continuous, and the unit circle is f([0,2π]) and so it's a compact set of R2 as image of the compact [0,2π] by the continuous function f.

$.$