کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4659775 | 1344336 | 2012 | 10 صفحه PDF | دانلود رایگان |
For a regular space X, X2 denotes the collection of all non-empty closed sets of X with the Vietoris topology and K(X) denotes the collection of all non-empty compact sets of X with the subspace topology of X2. In this paper, we will prove:
• K(γ) is orthocompact iff either or γ is a regular uncountable cardinal, as a corollary normality and orthocompactness of K(γ) are equivalent for every non-zero ordinal γ. We present its two proofs, one proof uses the elementary submodel techniques and another does not. This also answers Question C of Kemoto (2007) [4]. Moreover we discuss the natural question whether ω2 is orthocompact or not. We prove that
• ω2 is orthocompact iff it is countably metacompact,
• the hyperspace K(S) of the Sorgenfrey line S is orthocompact therefore so is the Sorgenfrey plane S2.
Journal: Topology and its Applications - Volume 159, Issue 4, 1 March 2012, Pages 1169-1178