Listing number

In mathematics, a Listing number of a topological space is one of several topological invariants introduced by the 19th-century mathematician Johann Benedict Listing and later given this name by Charles Sanders Peirce. 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.^[1]

There are four Listing numbers associated with a space.^[2] The smallest Listing number counts the number of connected components of a space, and is thus equivalent to the zeroth Betti number.^[3]