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{{short description|On decreasing nested sequences of non-empty compact sets}}
'''Cantor's intersection theorem''',<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Cantor's Intersection Theorem |url=https://mathworld.wolfram.com/CantorsIntersectionTheorem.html |access-date=2025-06-20 |website=mathworld.wolfram.com |language=en}}</ref> also called '''Cantor's nested intervals theorem''',<ref>{{Cite book |last=Segura |first=Julio |url=https://www.google.com.br/books/edition/An_Eponymous_Dictionary_of_Economics/Z6Oy4L-6LSwC |title=An Eponymous Dictionary of Economics: A Guide to Laws and Theorems Named After Economists |last2=Braun |first2=Carlos Rodríguez |date=2004-01-01 |publisher=Edward Elgar Publishing |isbn=978-1-84542-360-5 |pages=38 |language=en}}</ref><ref>{{Cite book |last=Denlinger |first=Charles G. |url=https://www.google.com.br/books/edition/Elements_of_Real_Analysis/CeTkVSXlj4cC |title=Elements of Real Analysis |date=2010-05-08 |publisher=Jones & Bartlett Publishers |isbn=978-1-4496-5993-6 |pages=103 |language=en}}</ref> refers to two closely related theorems in [[general topology]] and [[real analysis]], named after [[Georg Cantor]], about intersections of decreasing nested [[sequence|sequences]] of non-empty compact sets.
==Topological statement==
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