Nowhere dense set

From Citizendium
Revision as of 03:30, 21 February 2010 by Meg Taylor (Talk | contribs) (copyedit)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

In general topology, a nowhere dense set in a topological space is a set whose closure has empty interior.

An infinite Cartesian product of non-empty non-compact spaces has the property that every compact subset is nowhere dense.

A finite union of nowhere dense sets is again nowhere dense.

A first category space or meagre space is a countable union of nowhere dense sets: any other topological space is of second category. The Baire category theorem states that a non-empty complete metric space is of second category.

References

  • J.L. Kelley (1955). General topology. van Nostrand, 145,201.