turkmath.org

In this talk, the outstanding solution of the famous conjecture/question of Maurice Frechet, which asks whether $\ell_2$ is homeomorphic to $s$, i.e. the space of all real sequences, posed in 1928 will be given. Following its announcement, certain master mathematicians like Frechet himself, Bessaga, Klee, Pelczynski have all tried to solve this problem. Actually Mazur announced in 1932 that this conjecture was wrong. We just give the sketches of the affirmative and long proof of R.D. Anderson which was published in 1966. After this result of $\ell_2\cong s$ and by utilizing certain results of M. I. Kadec and C. Bessaga & A. Pelczynski, the following unbelievable conclusion is now obtained: Any separable infinite-dimensional Banach space and any separable infinite-dimensional Frechet space are topologically homeomorphic. It is in fact strange that most people working on Functional Analysis do still not know this result. We hope that this result becomes wellknown among the followers of Istanbul Analysis Seminars after this talk.