I am looking some reference, if it exist, that generalized the Moore`s characterization of the 2-sphere. To be more precise, Moore characterized 2-sphere by these two axioms: A space *X* is a 2-sphere if

*Jordan domain axiom*: For every simple closed curve*C*, the complement*X-C*consists of two connected components called*Jordan domains*bounded by*C*. Moreover, the boundary of Jordan domain bounded by*C*is exactly*C*.*Basic axiom*There is a countable basis of topology in*X*consisting of Jordan domains.

I took this two axioms from the paper *Moore`s Theorem - V. Timorin*. In this same paper, the author says that *R.H. Bing* gave a strong version of this characterization: a compact, connected, locally connected Hausdorff space *X* with more than one point is homeomorphic to the 2-sphere, provide that no embedded $\mathbb{S}^0$ separates *X*, and all embedded $\mathbb{S}^1$ separate *X*.

My question is: Is there any such characterization for closed surfaces of genus *g*?