On the finite support property of Gul'ko-Khmyleva's homeomorphism

It is established that for the homeomorphism of the spaces $c_0$ and $s \times c_0$ constructed by S.P. Gulko and T.E. Khmylyov, the image of the first coordinate functional under the adjoint mapping has no finite support. As a consequence, we see that this homeomorphism does not have the finite support property. In addition, it is shown that the images of all other coordinate functionals under the adjoint mapping have finite supports. The authors thank S.P. Gubko and T.E. Khmyleva, as well as A.V. Osipov for their kind attention to this work. The authors thank S.P. Gubko and T.E. Khmyleva, as well as A.V. Osipov for their kind attention to this work.