Let $(X,d)$ be a compact connected metric space with the property that for any distinct points $a,b$, $X\backslash \lbrace a,b\rbrace$ is disconnected. Clearly the unit circle has this property. Is there any other example (up to isomorphism) ??



A property of the unit circle
This property indeed characterizes the circle, but this is not obvious.


This was shown by R. L. Moore, according to Sam Nadler's *Continuum Theory* p. 156.


Added: the precise reference is [522] in [this historical survey](http://web.mst.edu/~wjcharat/JJC/publications/p138.pdf) of continuum theory.


