Enveloping Manifolds
نویسندگان
چکیده
We study the problem of embedding compact subsets of Rn into C1 submanifolds of minimal dimension. In [4], we define a generalized tangent space TxA suitable for a general compact subset A of Rn and we prove that A may be locally embedded into a C1 manifold of dimension dim(TxA). This result leads naturally to the global conjecture that for a compact subset A of Rn, there exists a C1 manifold M such that M ⊃ A and dimM = maxx∈A dim(TxA). We prove that this conjecture is false in general, but true if dim(TxA) is constant on A. Applications of these ideas to dimension theory, embedding theory, and dynamical systems are discussed.
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