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Boundary sets in the Hilbert cube |
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| Authors: | D. W. Curtis |
| Affiliation: | Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA |
| Abstract: | We study properties of those σZ-sets in the Hilbert cube whose complements are homeomorphic to Hilbert space. A characterization of such sets is obtained in terms of a proximate local connectedness property and a dense imbedding condition. Some examples and applications are given, including the formulation of a tower condition useful for recognizing (f-d) cap sets. |
| Keywords: | σZ-sets in the Hilbert cube (f-d) cap sets Hilbert space proximately LC∞ spaces |
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