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]

  1. ^ Peirce, Charles Sanders (1992), Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898, Harvard University Press, Footnote 70, pp. 279–280, ISBN 9780674749672.
  2. ^ Peirce, pp. 99–102.
  3. ^ Peirce, p. 99.