Hm? That looks backwards. [0,1] is a closed interval, (0,1) is an open interval. The former includes its boundary, the latter doesn’t. But a closed curve doesn

Hm? That looks backwards. [0,1] is a closed interval, (0,1) is an open interval. The former includes its boundary, the latter doesn’t. But a closed curve doesn’t mean the same thing as a curve which is a closed set. A closed curve is a continuous image of S^1 (the circle) , yeah?