# Is positively curved Alexandrov surface isometrically embeddable in R3\mathbb R^3?

I guess it is not. The example I have in mind is: $X^2$ is the spherical suspension of a circle $S^1(t)$ of length $0. Then $X$ has constant curvature =1 except at two suspension points, say $N$ and $S$.

But I cannot convince myself, since it seems this manifold can be approximated by a sequence of smooth Riemannian metrics $g_i$ with positive curvature by smoothing arbitrary small neighbourhood of $N$ and $S$, then by Pogorelov, if we assume sufficient smoothness on $g_i$, we get desired embedding by taking limit.