Listing number

{{Short description|Invariant of a topological space}}

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.{{citation|title=Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898|first=Charles Sanders|last=Peirce|authorlink=Charles Sanders Peirce|publisher=Harvard University Press|year=1992|isbn=9780674749672|at=Footnote 70, pp. 279–280|url=https://books.google.com/books?id=BWfRF5BAcG0C&pg=PA279}}.

There are four Listing numbers associated with a space.Peirce, pp. 99–102. The smallest Listing number counts the number of connected components of a space, and is thus equivalent to the zeroth Betti number.Peirce, p. 99.