Completeness properties of the generalized compact-open topology on partial functions with closed domains
✍ Scribed by L'ubica Holá; László Zsilinszky
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 182 KB
- Volume
- 110
- Category
- Article
- ISSN
- 0166-8641
No coin nor oath required. For personal study only.
✦ Synopsis
The primary goal of the paper is to investigate the Baire property and weak α-favorability for the generalized compact-open topology τ C on the space P of continuous partial functions f : A → Y with a closed domain A ⊂ X. Various sufficient and necessary conditions are given. It is shown, e.g., that (P, τ C ) is weakly α-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 corollaries we get sufficient conditions for Baireness and weak α-favorability of the graph topology of Brandi and Ceppitelli introduced for applications in differential equations, as well as of the Fell hyperspace topology. The relationship between τ C , the compact-open and Fell topologies, respectively is studied; moreover, a topological game is introduced and studied in order to facilitate the exposition of the above results.