Cantor's Intersection Theorem/Mistake

Source Work

2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.):

Cantor's Intersection Theorem


Mistake

In a ${}^*$complete metric space, a ${}^*$nested sequence (see nested sets) of subsets $\set {A_n}$ for which the ${}^*$diameters of $A_n$ tend to zero and contain a unique point of intersection.


Correction

The above is not a complete sentence.

It should say:

In a ${}^*$complete metric space, a ${}^*$nested sequence (see nested sets) of subsets $\set {A_n}$ for which the ${}^*$diameters of $A_n$ tend to zero contains a unique point of intersection.

... which is approximately how it is worded in the $5$th edition.


Sources

  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Cantor's Intersection Theorem
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