Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

All Cluster Points of Countable Sets in Supercompact Spaces are the Limits of Nontrivial Sequences

Zhongqiang Yang
Proceedings of the American Mathematical Society
Vol. 122, No. 2 (Oct., 1994), pp. 591-595
DOI: 10.2307/2161053
Stable URL: http://www.jstor.org/stable/2161053
Page Count: 5
  • Read Online (Free)
  • Download ($30.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
All Cluster Points of Countable Sets in Supercompact Spaces are the Limits of Nontrivial Sequences
Preview not available

Abstract

A space is called supercompact if it has an open subbase such that every cover consisting of elements of the subbase has a subcover consisting of two elements. In this paper we prove that, in a continuous image of a closed Gδ-set of a supercompact space, a point is a cluster point of a countable set if and only if it is the limit of a nontrivial sequence. As corollaries, we answer questions asked by J. van Mill et al.

Page Thumbnails

  • Thumbnail: Page 
591
    591
  • Thumbnail: Page 
592
    592
  • Thumbnail: Page 
593
    593
  • Thumbnail: Page 
594
    594
  • Thumbnail: Page 
595
    595