In mathematics, the caliber or calibre of a

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...

''X'' is a

cardinal Cardinal or The Cardinal may refer to: Animals * Cardinal (bird) or Cardinalidae, a family of North and South American birds **''Cardinalis'', genus of cardinal in the family Cardinalidae **''Cardinalis cardinalis'', or northern cardinal, the ...

''κ'' such that for every set of ''κ'' nonempty open subsets of ''X'' there is some point of ''X'' contained in ''κ'' of these subsets. This concept was introduced by . There is a similar concept for posets. A pre-caliber of a poset ''P'' is a cardinal ''κ'' such that for any collection of elements of ''P'' indexed by ''κ'', there is a subcollection of cardinality ''κ'' that is centered. Here a subset of a poset is called centered if for any finite subset there is an element of the poset less than or equal to all of them.

References

* *{{citation, mr=0027310 , last=Shanin, first= N. A. , title=On the product of topological spaces , journal=Trudy Mat. Inst. Steklov. , volume=24, year=1948 Topology