Notes on C_\lambda(X)
by
N. V. Velichko
Institute of Mathematics and Mechanics UB RAS

C_\lambda(X) is the space of continuous real-valued functions on X with the topology of uniform convergence on \lambda, where \lambda is a family of bounded sets of X.

It is proved that C_\lambda(X)) is separable iff X is condenced on a second-countable space. Have constructed a space of countable network weight such that C_\lambda(X)) has not any countable network.

Date received: June 2, 1998

Copyright © 1998 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 # cabc-21.