We present a brane-world scenario in which two regions of $AdS_5$ space-time are glued together along a 3-brane with constant positive curvature such that {em all} spatial dimensions form a compact manifold of topology $S^4$. It turns out that the induced geometry on the brane is given by Einsteins static universe. It is possible to achieve an anisotropy of the manifold which allows for a huge hierarchy between the size of the extra dimension $R$ and the size of the observable universe $R_U$ at present. This anisotropy is also at the origin of a very peculiar property of our model: the physical distance between {em any two points} on the brane is of the order of the size of the extra dimension $R$ regardless of their distance measured with the use of the induced metric on the brane. In an intermediate distance regime $R ll r ll R_U$ gravity on the brane is shown to be effectively 4-dimensional, with corresponding large distance corrections, in complete analogy with the Randall-Sundrum II model. For very large distances $r sim R_U$ we recover gravity in Einsteins static universe. However, in contrast to the Randall-Sundrum II model the difference in topology has the advantage of giving rise to a geodesically complete space.
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