Completeness properties of the generalized compact-open topology on partial maps
by
László Zsilinszky
University of North Carolina at Pembroke
Coauthors: Lubica Holá

Results on Baireness and weak \alpha-favorability of the generalized compact-open topology \tau_C on the space \Cal P of continuous partial functions f:A --> Y with closed domains A subset X will be presented; e.g. that (\Cal P, \tau_C) is weakly \alpha-favorable (and hence a Baire space), if X is a locally compact paracompact space and Y is a regular space having a completely metrizable dense subspace. As colloraries we get sufficient conditions for Baireness and weak \alpha-favorability of the Fell hyperspace topology as well as of the graph topology of Brandi and Ceppitelli introduced for applications in differential equations.

Two approaches are explored: one of them makes use of the favorable connection that exists (under certain restrictions on X and Y) between \tau_C, the compact-open topology \tau_CO and the Fell topology \tau_F, respectively, and allows us to utilize earlier results of McCoy, Ntantu, Ma and Gruenhage on \tau_CO and other results on \tau_F. The second approach relies on some game-theoretical conditions on X and Y that ensure Baireness and weak \alpha-favorability of the generalized compact-open topology. The theorems resulting from these approaches overlap but, surprisingly, do not follow from each other and hence could be of independent interest.

Date received: March 13, 1999

Copyright © 1999 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 # caca-68.