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Let G be a Lie group and let rho be a group representation of G on C^n (for some natural number n), which is continuous in the sense that the function G×C^n->C^n defined by ...

If a function f(x) is continuous on a closed interval [a,b], then f(x) has both a maximum and a minimum on [a,b]. If f(x) has an extremum on an open interval (a,b), then the ...

"Stampacchia's theorem" is a name given to any number of related results in functional analysis, and while the body of the theorem often varies depending on the literature ...

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 ...

Fubini's theorem, sometimes called Tonelli's theorem, establishes a connection between a multiple integral and a repeated one. If f(x,y) is continuous on the rectangular ...

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 ...

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 ...

If g is a continuous function g(x) in [a,b] for all x in [a,b], then g has a fixed point in [a,b]. This can be proven by supposing that g(a)>=a g(b)<=b (1) g(a)-a>=0 ...

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