کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424751 | 1344321 | 2012 | 8 صفحه PDF | دانلود رایگان |
We show in ZF that:(i)A countably compact metric space need not be limit point compact or totally bounded and, a limit point compact metric space need not be totally bounded.(ii)A complete, totally bounded metric space need not be limit point compact or Cantor complete.(iii)A Cantor complete, totally bounded metric space need not be limit point compact.(iv)A second countable, limit point compact metric space need not be totally bounded or Cantor complete.(v)A sequentially compact, selective metric space (the family of all non-empty open subsets of the space has a choice function) is compact.(vi)A countable product of sequentially compact (resp. compete and totally bounded) metric spaces is sequentially compact (resp. compete and totally bounded).
Journal: Topology and its Applications - Volume 159, Issue 16, 1 October 2012, Pages 3396-3403