Every RCD space with curvature bounded above is a topological manifold with boundary whose interior is the regular set, a smooth geodesically convex manifold.
Berestovski , Busemann spaces with upper-bounded A leksandrov curvature , Algebra i Analiz 14 (2002), no
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On the structure of RCD spaces with upper curvature bounds
Every RCD space with curvature bounded above is a topological manifold with boundary whose interior is the regular set, a smooth geodesically convex manifold.