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If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

The converse of Fisher's theorem.

There are several theorems that generally are known by the generic name "Pappus's Theorem." They include Pappus's centroid theorem, the Pappus chain, Pappus's harmonic ...

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...

The reciprocity theorem for x^8=q (mod p).

A Radon measure is a Borel measure that is finite on compact sets.

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...