View source for Helly number

$
  \def\X{\mathcal X}         % family of sets
  \def\S{\mathcal S}         % subfamily
$

The '''Helly number''' $ H(\X) $ of a family of sets $\X$ is
(in analogy to [[Helly's theorem]]) the smallest natural number $k$
such that the following (compactness-type) intersection property holds:

: Let $ \S $ be a subfamily of $ \X $. If any $k$ members of $\S$ have a common point, then the sets of $\S$ have a common point.

This is also called the ''Helly property'', and 
the corresponding is called a ''Helly family'' (of order $k$).