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Difference between revisions of "Everywhere-dense set"

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''<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366601.png" /> in a topological space <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366602.png" />''
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#REDIRECT[[Dense set]]
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A set described by the property <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366603.png" />, where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366604.png" /> denotes the closure of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366605.png" />. In other words, any set open in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366606.png" /> contains at least one point of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e036/e036660/e0366607.png" />. The term  "dense set in a topological spacedense set"  is also employed.
 

Latest revision as of 17:26, 22 September 2012

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How to Cite This Entry:
Everywhere-dense set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Everywhere-dense_set&oldid=15938
This article was adapted from an original article by A.A. Mal'tsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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