کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424635 | 1344250 | 2015 | 10 صفحه PDF | دانلود رایگان |
The hyperspace of nontrivial convergent sequences of a metric space X without isolated points will be denoted by Sc(X). This hyperspace is equipped with the Vietoris Topology. It is not hard to prove that Sc([0,1]) and Sc(I) are not homeomorphic, where I are the irrationals. We show that the hyperspaces Sc(R) and Sc([0,1]) are path-wise connected. In a more general context, we show that if X is path-wise connected space, then Sc(X) is connected. But Sc(X) is not necessarily path-wise connected even when X is the Warsaw circle. These make interesting to study the connectedness of the hyperspace of nontrivial convergent sequences in the realm of continua. Also, we prove that if X is a second countable space, then Sc(X) is meager. We list several open questions concerning this hyperspace.
Journal: Topology and its Applications - Volume 196, Part B, December 2015, Pages 795-804