On spaces of inverse limits
by
Jacek Nikiel
American University of Beirut
Coauthors: H.M. Tuncali, E.D.Tymchatyn

Let {X_\alpha : \alpha in A} be a family of spaces labelled by elements of a directed set (A, <= ).

Let I be the family of all subsets [?] of the product space X = \Pi_{\alpha in A} X_\alpha such that there exist continuous functions f_\beta^\alpha : X_\alpha --> X^\beta, for \beta <= \alpha in A, such that the following two conditions are satisfied:

1. f_\alpha^\alpha = id_X\alpha for each \alpha,
2. f_\gamma^\beta o f_\beta^\alpha = f_\gamma^\alpha when \gamma <= \beta <= \alpha,
3. [?] = lim _<-- (X_\alpha, f_\beta^\alpha, A).

The case when all spaces X_\alpha are compact metrizable and I is treated as a subspace of the hyperspace 2^X is studied.

This is the joint work with H.M.Tuncali and E.D.Tymchatyn.

Date received: January 31, 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 Conferences Inc. Document # caaa-26.