Open (Geometry)

Pronunciation: /ˈoʊ pən/ ?

A geometric figure is open if any part of the boundary of the figure is not part of the figure.
Figure 1: An open geometric figure	The clearest example of this is a graph of inequalities. Figure 1 is the graph of a system of inequalities. The points on the line y < 3 - x are not part of the boundary. Since the inequality y < 3 - x does not include the points on the line, the shaded geometric figure is open.
Figure 2: A closed geometric figure	In figure 2, the inequality y <= 3 - x does include the points on the line, so the shaded geometric figure is not open.

References

1. open. merriam-webster.com. Encyclopedia Britannica. (Accessed: 2009-03-12). http://www.merriam-webster.com/dictionary/open.

More Information

• McAdams, David. Closed (sets). allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Closed%20(sets).
• McAdams, David. Closed (geometry). allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Closed%20(Geometry).

Cite this article as:

Open (Geometry). 2010-10-02. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/g/g_open.html.

Translations

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Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Revision History

2010-10-02: Clarified definition. (McAdams, David.)
2008-08-02: Added dictionary.com to More Information (McAdams, David.)
2008-06-11: Added hot link for inequality (McAdams, David.)
2007-07-30: Initial version (McAdams, David.)