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On the Deleted Product Criterion For Embeddability in

Authors:	A Skopenkov

Institution:	Chair of Differential Geometry, Department of Mechanics and Mathematics, Moscow State University, Moscow,119899, Russia

Abstract:	For a space let $\tilde K=\{(x,y)\in K\times K\| x\not =y\}$ . Let $\mathbb{Z}_{2}$ act on $\tilde K$ and on $S^{m-1}$ by exchanging factors and antipodes respectively. We present a new short proof of the following theorem by Weber: For an -polyhedron and $m\geqslant \frac{3(n+1)}{2}$ , if there exists an equivariant map $F:\nobreak \tilde K\rightarrow S^{m-1}$ , then is embeddable in $\mathbb{R}^{m}$ . We also prove this theorem for a peanian continuum and . We prove that the theorem is not true for the 3-adic solenoid and .

Keywords:	Embedding deleted product engulfing quasi-embedding metastable case peanian continua 3-adic solenoid relative regular neighborhood

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