On subspaces of exp(N)
by
Andrzej Szymanski
Slippery Rock University
Coauthors: M. Ismail (Silesian University), Sz. Plewik (Slippery Rock University)

This is a report on my joint paper with M.Ismail and Sz.Plewik.

Let exp(X) denote the exponential space of a topological space X. We study the subspaces of the space exp(N), where N = { 1, 2, 3, ... } is the discrete space of natural numbers. In particular, we show that any metrizable subspace of exp(N) is \sigma-discrete. We also show that if the metrizability number of exp(X) is countable, then X (and exp(X)) must be compact and and metrizable.

Date received: June 30, 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-59.