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Difference between revisions of "Subbase"

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A family <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074270/p0742701.png" /> of open subsets of a [[Topological space|topological space]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074270/p0742702.png" /> such that the totality of all sets which are intersections of a finite number of elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074270/p0742703.png" /> forms a [[Base|base]] of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p074/p074270/p0742704.png" />.
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A family $\gamma$ of open subsets of a [[Topological space|topological space]] $X$ such that the totality of all sets which are intersections of a finite number of elements of $\gamma$ forms a [[Base|base]] of $X$.
  
  

Revision as of 12:20, 12 April 2014

A family $\gamma$ of open subsets of a topological space $X$ such that the totality of all sets which are intersections of a finite number of elements of $\gamma$ forms a base of $X$.


Comments

The Western term is subbase.

References

[a1] R. Engelking, "General topology" , Heldermann (1989)
How to Cite This Entry:
Subbase. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Subbase&oldid=31622
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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