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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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Chain of interior of closed set

It is well known that a topological space with asending chain condition for open subsets is called Noetherian. Is there any characterizations or a nice property for a Hausdorff topological space such …
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