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We establish the asymptotic regularity and the $\Delta$-convergence of thesequence constructed by the alternating projections to closed convex sets in aCAT($\kappa$) space with $\kappa > 0$. Furthermore, the strong convergence ofthe alternating von Neumann sequence is presented under certain regularity orcompactness.

Convergences of Alternating Projections in CAT($\kappa$) Spaces