3 Counterexample to Theorem 2.2 (part (1)) for card (E)> d See [39]

We observe immediately the restriction k less-than-or-equal-to d (recall k equals normal c normal a normal r normal d left-parenthesis upper E right-parenthesis for the existence of the extension normal upper Phi in Theorem 2.2 (part (1)). Is this simply a “technical issue”? The answer to this “optimistic” guess is no.

The k less-than-or-equal-to d sufficient condition for the existence of the extension normal upper Phi turns out to be deeper than merely “sufficient” as a tool. In fact, under the geometry of upper E given by Theorem 2.2, the extension normal upper Phi does not always exist for k > d. In this chapter we will provide the required counterexample. In fact, the  >  case under the geometry of the finite ...

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