We study the topology of a Ricci limit space
(
X
,
p
)
(X,p)
, which is the Gromov-Hausdorff limit of a sequence of complete
n
n
-manifolds
(
M
i
,
p
i
)
(M_i, p_i)
with
R
i
c
≥
−
(
n
−
1
)
\mathrm {Ric}\ge -(n-1)
. Our first result shows that, if
M
i
M_i
has Ricci bounded covering geometry, i.e. the local Riemannian universal cover is non-collapsed, then
X
X
is semi-locally simply connected. In the process, we establish a slice theorem for isometric pseudo-group actions on a closed ball in the Ricci limit space. In the second result, we give a description of the universal cover of
X
X
if
M
i
M_i
has a uniform diameter bound; this improves a result by Ennis and Wei [Differential Geom. Appl. 24 (2006), pp. 554-562].