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Open covers and the square bracket partition relation |
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| Authors: | Marion Scheepers |
| Affiliation: | Department of Mathematics and Computer Science Boise State University Boise, Idaho 83725 |
| Abstract: | An open cover  of an infinite separable metric space  is an  -cover of  if  and for every finite subset  of  there is a  such that  . Let  be the collection of  -covers of  . We show that the partition relation ![$Omega rightarrow[Omega ]^2_2$](http://www.ams.org/proc/1997-125-09/S0002-9939-97-03898-7/gif-abstract/img13.gif) holds if, and only if, the partition relation ![$Omega rightarrow[Omega ]^2_3$](http://www.ams.org/proc/1997-125-09/S0002-9939-97-03898-7/gif-abstract/img14.gif) holds. |
| Keywords: | Rothberger property square bracket partition relation Ramsey's theorem |
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