To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

From Wikipedia, the free encyclopedia

A star domain (equivalently, a star-convex or star-shaped set) is not necessarily convex in the ordinary sense.
A star domain (equivalently, a star-convex or star-shaped set) is not necessarily convex in the ordinary sense.
An annulus is not a star domain.
An annulus is not a star domain.

In mathematics, a set S in the Euclidean space Rn is called a star domain (or star-convex set, star-shaped set or radially convex set) if there exists an x0 in S such that for all x in S the line segment from x0 to x is in S. This definition is immediately generalizable to any real or complex vector space.

Intuitively, if one thinks of S as of a region surrounded by a wall, S is a star domain if one can find a vantage point x0 in S from which any point x in S is within line-of-sight. A similar, but distinct, concept is that of a radial set.


  • Any line or plane in Rn is a star domain.
  • A line or a plane with a single point removed is not a star domain.
  • If A is a set in Rn, the set obtained by connecting all points in A to the origin is a star domain.
  • Any non-empty convex set is a star domain. A set is convex if and only if it is a star domain with respect to any point in that set.
  • A cross-shaped figure is a star domain but is not convex.
  • A star-shaped polygon is a star domain whose boundary is a sequence of connected line segments.


  • The closure of a star domain is a star domain, but the interior of a star domain is not necessarily a star domain.
  • Every star domain is a contractible set, via a straight-line homotopy. In particular, any star domain is a simply connected set.
  • Every star domain, and only a star domain, can be "shrunken into itself"; that is, for every dilation ratio r < 1, the star domain can be dilated by a ratio r such that the dilated star domain is contained in the original star domain.[1]
  • The union and intersection of two star domains is not necessarily a star domain.
  • A non-empty open star domain S in Rn is diffeomorphic to Rn.

See also


  1. ^ Drummond-Cole, Gabriel C. "What polygons can be shrinked into themselves?". Math Overflow. Retrieved 2 October 2014.

External links

This page was last edited on 15 November 2020, at 14:09
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.