# Cantor axiom

From Encyclopedia of Mathematics

One of the axioms characterizing the completeness of the real line (cf. Continuity axiom). It states that any nested sequence of closed intervals (that is, each interval is contained in its predecessor) with lengths tending to zero contains a unique common point. Formulated by G. Cantor, 1872.

**How to Cite This Entry:**

Cantor axiom.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Cantor_axiom&oldid=43156

This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article