کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424677 | 1344250 | 2015 | 23 صفحه PDF | دانلود رایگان |
We introduce a new approach to the construction of group topologies on free abelian groups which are productively countably compact. We construct an example as in the title (using c incomparable selective ultrafilters) that closes the gap between results of Tkachenko (1990) [9] that showed the free abelian group of cardinality c admits a countably compact group topology using CH and Tomita (1998) [11] that showed a free abelian group cannot be endowed with a group topology that makes its infinite countable power countably compact. This is also connected to Comfort's question 477 in the Open Problems in Topology on countable compactness of powers. In fact, it is the first torsion free example of a topological group whose least power that fails to be countably compact is Ï.
Journal: Topology and its Applications - Volume 196, Part B, December 2015, Pages 976-998