  A local cut point is by definition a point that disconnectes its sufficiently
small neighborhood. We show that there exists an upper bound for the degree of
a local cut point in a metric measure space satisfying the generalized
Bishop--Gromov inequality. As a corollary, we obtain an upper bound for the
number of ends of such a space. We also obtain some obstruction conditions for
the existence of a local cut point in a metric measure space satisfying the
Bishop--Gromov inequality or the Poincar\'{e} inequality. For example, the
measured Gromov--Hausdorff limits of Riemannian manifolds with a lower Ricci
curvature bound satisfy these two inequalities.
