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We point out that a 4-dimensional topological manifold with an Alexandrovmetric (of curvature bounded below) and with an effective, isometric action ofthe circle or the 2-torus is locally smooth. This observation implies that thetopological and equivariant classifications of compact, simply connectedRiemannian 4-manifolds with positive or nonnegative sectional curvature and aneffective isometric action of a circle or a 2-torus also hold if we considerAlexandrov manifolds instead of Riemannian manifolds.

Simply connected Alexandrov 4-manifolds with positive or nonnegative curvature and torus actions