Let $S^1$ denote the unit circle in the plane $\Bbb R^2$. Pick out the true statement(s):
(a) There exists $f : S^1 \to\Bbb R$ which is continuous and one-one.
(b) For every continuous function $f : S^1 \to\Bbb R$, there exist uncountably many pairs of distinct points $x$ and $y$ in $S^1$ such that $f(x) = f(y)$.
(c) There exists $f : S^1 \to\Bbb R$ which is continuous and one-one and onto.
I have only idea that for (c) $f$ is nearly homeomorphism as we cant say that $f$ inverse is continuous or not and the sets are not homeomorphic. No idea about (a) and (b).