On the Deleted Product Criterion for Embeddability in R
نویسنده
چکیده
For a space K let K̃ = {(x, y) ∈ K ×K|x 6= y}. Let Z2 act on K̃ and on Sm−1 by exchanging factors and antipodes respectively. We present a new short proof of the following theorem by Weber: For an n-polyhedron K and m > 3(n+1) 2 , if there exists an equivariant map F : K̃ → Sm−1, then K is embeddable in Rm. We also prove this theorem for a peanian continuum K and m = 2. We prove that the theorem is not true for the 3-adic solenoid K and m = 2.
منابع مشابه
Eliminating Higher-Multiplicity Intersections, II. The Deleted Product Criterion in the r-Metastable Range
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