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It was shown in [A. Mondino and G. Wei, On the universal cover and the fundamental group of anRCD*⁢(K,N){\rm RCD}^{*}(K,N)-space, J. reine angew. Math. 753 2019, 211–237] that anyRCD*⁢(K,N){\mathrm{RCD}^{*}(K,N)}space(X,d,){(X,d,\mathfrak{m})}has a universal cover. We prove that for any pointx∈X{x\in X}andR&gt;0{R&gt;0}, there existsr&lt;R{r&lt;R}such that any loop inBr⁢(x){B_{r}(x)}is contractible inBR⁢(x){B_{R}(x)}; in particular,  X  is semi-locally simply connected and the universal cover of  X  is simply connected. This generalizes the earlier work in [J. Wang, Ricci limit spaces are semi-locally simply connected, preprint 2021] that any Ricci limit space is semi-locally simply connected.

RCD * ( K , N ) spaces are semi-locally simply~connected