Abstract
A DC-set is a set defined by means of convex constraints and one additional inverse convex constraint. Given an arbitrary closed subsetM of the Euclideann-space, we show that there exists a DC-set in (n+1)-space being homeomorphic to the given setM. Secondly, for any fixedn⩾2, we construct a compactn-dimensional manifold with boundary, which is a DC-set and which has arbitrarily large Betti-numbersr k fork ⩽ n−2.
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Günzel, H., Hirabayashi, R., Jongen, H.T. et al. On the topological complexity of DC-sets. J Glob Optim 4, 279–284 (1994). https://doi.org/10.1007/BF01098362
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DOI: https://doi.org/10.1007/BF01098362