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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
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Infinitely generated Kleinian groups
If in the original question we replace limit set by radial limit set than the answer is yes by the two Sullivan's theorems. So in your exmple there are planty of non-radial limit points. What types ar …