Εισήγηση 5: Involutions and fredholm maps
Από τα πρακτικά του Χρονικά 4ου Πανελλήνιου Μαθηματικού Συνεδρίου - Χρονικά 4ου Πανελλήνιου Μαθηματικού Συνεδρίου
Consider a map f:S^n->R^k. By the classical Borsuk - Ulam theorem of n>=k, then there are points xεS^n such that f(x)=f(-x). More precisely the set A(f)={xεS^n|f(x)=f(-x)} has covering dimension >=n-k. This result has been refined and generalized by different authors mainly to the case where R^n is replaced by a manifold M^n with involution or with a freely acting finite group. In this paper the problem of estimating A(f), is considered again, but this time in an ifinite dimensional setting.
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