Linear Topological Classification of Certain Function Spaces
by
Kazuhiko Morishita
Ashikaga Institute of Technology, Japan

Let C_p(X) be the space of all continuous real-valued functions on a Tychonoff space X with the pointwise convergent topology. Two Tychonoff spaces X and Y are said to be l-equivalent if C_p(X) and C_p(Y) are linearly homeomorphic. In 1980, Pavlovski showed that, for two finite polyphedra X and Y, X and Y are l-equivalent if and only if dimX coincides with dimY. Subsequently, the classification problem of certain classes of spaces up to l-equivalence has been studied by several general topologists. For zero-dimensional separable metrizable spaces, some exact results in this direction have been known. This talk will present some results for non-zero dimensional spaces. For nice spaces; compact topological manifolds and CW complexes, we have complete answers for the problem.

Date received: June 25, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-36.