Badly Noncontinuous Injective Operators Between Polish Metric Linear Spaces
by
Z. Lipecki

Let X and Z be infinite-dimensional Polish metric linear spaces. There exists an injective linear operator T from X into Z such that no restriction of T to a subspace Y of X with dim Y = c is continuous. This strengthens and generalizes a result of M. I. Ostrovskii (1992) which was concerned with Banach spaces. The latter was obtained in response to a question asked by V. I. Bogachev, B. Kirchheim and W. Schachermayer (1989). Besides, our result was inspired by the classical theorem of W. Sierpinski and A. Zygmund (1923) to the effect that there exists a function f from R into R such that no restriction of f to a subset E of R with card E = c is continuous.

Date received: June 24, 1996

Copyright © 1996 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 Mathematical Conference Abstracts. Document # caai-64.