Helly's theorem

The set of Helly is a mathematical theorem, which goes back to the Austrian mathematician Eduard Helly. The phrase is attributed to the field of convex geometry. Here he is closely associated with a number of other classical theorems. Its effect extends to other areas of mathematics such as discrete mathematics, where he became the starting point for the study of quantity systems with the so-called Helly property.

Wording of the sentence

The set of Helly can be formulated as follows:

In other formulation can also be expressed by the set of Helly:

The general requirements listed above will even weaken, and that to the extent that is required only for the infinite case:

History, evidence, related results

The first proof of the theorem of Helly gave the Austrian mathematician Johann Radon in 1921. He used a result which is known as the Radon today. Eduard Helly had, however, the record is found already at the latest in 1913, Johann Radon proved the sentence only after Eduard Helly had pointed out to him. Eduard Helly even published in the episode two of his own works, which give a different approach to this issue. Other authors further evidence yet been found. The set of Helly is also an important tool in the proof of other classical theorems of convex geometry, such as the set of Krasnoselskii or the set of Jung.

Demarcation

There are in calculus another set of Helly, which is also known as selection set from Helly or in the English literature as Helly's selection theorem. This treats the convergence of sequences of functions.