In mathematics, a Listing number 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 po ...

is one of several

topological invariant In topology and related areas of mathematics, a topological property or topological invariant is a property of a topological space that is invariant under homeomorphisms. Alternatively, a topological property is a proper class of topological space ...

s introduced by the 19th-century mathematician

Johann Benedict Listing Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician. J. B. Listing was born in Frankfurt and died in Göttingen. He first introduced the term "topology" to replace the older term "geometria situs" (also called ...

and later given this name by

Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for t ...

. Unlike the later invariants given by Bernhard Riemann, the Listing numbers do not form a complete set of invariants: two different two-dimensional manifolds may have the same Listing numbers as each other. There are four Listing numbers associated with a space. The smallest Listing number counts the number of connected components of a space, and is thus equivalent to the zeroth

Betti number In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of ''n''-dimensional simplicial complexes. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplici ...

.Peirce, p. 99.

References

Topology Charles Sanders Peirce {{topology-stub