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Hurewicz Sets of Reals without Perfect Subsets
| Content Provider | Semantic Scholar |
|---|---|
| Author | Repovvs, Duvsan D. Tsaban, Boaz Zdomskyy, Lyubomyr |
| Copyright Year | 2008 |
| Abstract | We show that even for subsets X of the real line that do not contain perfect sets, the Hurewicz property does not imply the property S 1 (Γ, Γ), asserting that for each countable family of open γ-covers of X, there is a choice function whose image is a γ-cover of X. This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszynski and the second author, and implies that for Cp(X), the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangel'skii's property α 2 . |
| Starting Page | 2515 |
| Ending Page | 2520 |
| Page Count | 6 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/s0002-9939-08-09193-4 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/2008-136-07/S0002-9939-08-09193-4/S0002-9939-08-09193-4.pdf |
| Alternate Webpage(s) | http://u.cs.biu.ac.il/~tsaban/Pdf/PublishedBackUp/HurperfBU.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0612148v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0612148v2.pdf |
| Alternate Webpage(s) | https://arxiv.org/pdf/math/0612148v5.pdf |
| Alternate Webpage(s) | https://www.ams.org/proc/2008-136-07/S0002-9939-08-09193-4/S0002-9939-08-09193-4.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0612148v3.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/s0002-9939-08-09193-4 |
| Volume Number | 136 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
