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Difference between revisions of "Hausdorff axiom"

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One of the separation axioms (cf. [[Separation axiom|Separation axiom]]). It was introduced by F. Hausdorff in 1914 (see [[#References|[1]]]) in his definition of the concept of a topological space. The Hausdorff axiom holds in a topological space if any two (distinct) points of it have disjoint neighbourhoods. A space satisfying the Hausdorff axiom is called a Hausdorff space or a <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/h/h046/h046680/h0466802.png" />-space.
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One of the separation axioms (cf. [[Separation axiom|Separation axiom]]). It was introduced by F. Hausdorff in 1914 (see [[#References|[1]]]) in his definition of the concept of a topological space. The Hausdorff axiom holds in a topological space if any two (distinct) points of it have disjoint neighbourhoods. A space satisfying the Hausdorff axiom is called a Hausdorff space or a $T_2$-space.
  
 
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Latest revision as of 16:40, 20 April 2014

One of the separation axioms (cf. Separation axiom). It was introduced by F. Hausdorff in 1914 (see [1]) in his definition of the concept of a topological space. The Hausdorff axiom holds in a topological space if any two (distinct) points of it have disjoint neighbourhoods. A space satisfying the Hausdorff axiom is called a Hausdorff space or a $T_2$-space.

References

[1] F. Hausdorff, "Set theory" , Chelsea, reprint (1978) (Translated from German)


Comments

References

[a1] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)
How to Cite This Entry:
Hausdorff axiom. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Hausdorff_axiom&oldid=16110
This article was adapted from an original article by I.G. Koshevnikova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article