Pseudocompact spaces and -spaces ![](/proc/2004-132-06/S0002-9939-04-07279-X/gif-title0/img3.gif) |
| |
Authors: | Jerzy Kakol Stephen A Saxon Aaron R Todd |
| |
Institution: | Department of Mathematics, Baruch College, C.U.N.Y., New York, New York 10010, and Faculty of Mathematics and Informatics, A. Mickiewicz University, 60-769 Poznan, Matejki 48-49, Poland ; Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611-8105 ; Department of Mathematics, Baruch College, C.U.N.Y., New York, New York 10010 |
| |
Abstract: | Let be a completely regular Hausdorff space, and let be the space of continuous real-valued functions on endowed with the compact-open topology. We find various equivalent conditions for to be a -space, resolving an old question of Jarchow and consolidating work by Jarchow, Mazon, McCoy and Todd. Included are analytic characterizations of pseudocompactness and an example that shows that, for , Grothendieck's -spaces do not coincide with Jarchow's -spaces. Any such example necessarily answers a thirty-year-old question on weak barrelledness properties for , our original motivation. |
| |
Keywords: | Compact-open topology $DF\ $- and $df$-spaces completely regular docile locally complete weak barrelledness |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 |
|