APPLYING COORDINATE PRODUCTS TO THE TOPOLOGICAL IDENTIFICATION OF NORMED SPACES

Using the l2-products we find pre-Hilbert spaces that are absorbing se ts for all Borelian classes of order alpha greater-than-or-equal-to 1 . We also show that the following spaces are homeomorphic to SIGMA(inf inity), the countable product of the space SIGMA = {(x(n)) is-an-eleme nt-of R(infinity) : (x(n)) is bounded} : (1) every coordinate product PI(C) H(n) of normed spaces H(n) in the sense of a Banach space C , wh ere each H(n) is an absolute F(sigmadelta)-set and infinitely many of the H(n) 's are Z(sigma)-spaces, (2) every function space L(p) = and(p '<p) L(p') with the L(q)-topology, 0 < q < p less-than-or-equal-to inf inity. (3) every sequence space l(p) = and(p<p') l(p') with the l(q)-t opology, 0 less-than-or-equal-to p < q < infinity. We also note that e ach additive and multiplicative Borelian class of order alpha greater- than-or-equal-to 2 , each projective class, and the class of nonprojec tive spaces contain uncountably many topologically different pre-Hilbe rt spaces which are Z(sigma)-spaces.