## A converse of a theorem of R. H. Bing and its generalization: technical note |

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2-sphere Air Force Base Air Force Office Alexander Duality Theorem Applied Mathematics arbitrary given Arlington Hall Station Base Ohio Attn Bing announced Cantor set closed and totally closed subset Commander Air Force common boundary connected continuum forming connectedness copies cycle Zr D. C. Administered D. C. Attn denote Department of Mathematics DISTRIBUTION LIST Continued exists a closed exists an e-transformation Force Base Ohio forming a common given complementary domains given positive number Hi(c homeomorphism hypothesis Illinois Department Lemma locally compact locally separate manifold Massachusetts MATHEMATICAL SCIENCES DIRECTORATE MATHEMATICS Technical Note Mathematics University N. W. Washington 25 North Carolina Office of Scientific open subset Operations Analysis orientable closed 2-manifold q in S(x r-separating set R. H. Bing s-transformation f(C SCIENCES DIRECTORATE AIR Standards Washington 25 Technical Library THEOREM OF R. H. totally disconnected subset UNIVERSITY OF MICHIGAN University of Minnesota Wright-Patterson Air Force x2 lie xi and x2