I note that someone did ask a similar question here (Thin indifference curves), but I didn't fully understand the answer, and my question refers specifically to my textbook.
In my textbook, Jehle & Reny, the axiom of continuity is defined as follows:
Why does continuity alone preclude an indifference region with "thickness"? I would've thought the preference relation for a consumer who is indifferent between all combinations of x1 and x2 still satisfies continuity, and that non-satiation is required to rule out "thick" indifference curves.
Am I misunderstanding something (highly likely)?