Talk:Boundary point

From Citizendium
Revision as of 04:18, 4 October 2009 by imported>Boris Tsirelson (→‎every point is a boundary case: new section)
Jump to navigation Jump to search
This article is developing and not approved.
 Main Article
 Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
To learn how to update the categories for this article, see here. To update categories, edit the metadata template.
 Definition:  (of a set) In geometry and topology, a point such that every neighbourhood contains both points in the set and points not in the set. [d] [e]
Checklist and Archives
 Workgroup category:  Mathematics [Please add or review categories]
 Talk Archive:  none  English language variant:  British English

every point is a boundary case

"...every point is a boundary case, or there is no boundary point at all — are both possible. In the first case the set is said to be dense in the space" — Really? The whole space is a (trivial) example of a dense set, but belongs to the latter case, not the former one. The condition "every point of the space is a boundary point of the given set" is equivalent rather to "the given set and its complement are both dense". Boris Tsirelson 09:18, 4 October 2009 (UTC)

Retrieved from "https://citizendium.org/wiki/index.php?title=Talk:Boundary_point&oldid=693148"