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Most of results of Bestvina and Mogilski [Characterizing certain incomplete infinite-dimensional absolute retracts. Michigan Math. J., 33, 291–313 (1986)] on strong Z-sets in ANR’s and absorbing sets is generalized to nonseparable case. It is shown that if an ANR X is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and w(U) = w(X) (where “w” is the topological weight) for...
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