In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space.[1] A graphical illustration of a nildimensional space is a point.[2]



The three notions above agree for separable, metrisable spaces.[citation needed][clarification needed]

Properties of spaces with small inductive dimension zero


All points of a zero-dimensional manifold are isolated.

In particular, the zero-dimensional hypersphere is a pair of points, and the zero-dimensional ball is a single point.



  1. ^ Hazewinkel, Michiel (1989). Encyclopaedia of Mathematics, Volume 3. Kluwer Academic Publishers. p. 190. ISBN 9789400959941.
  2. ^ Wolcott, Luke; McTernan, Elizabeth (2012). "Imagining Negative-Dimensional Space" (PDF). In Bosch, Robert; McKenna, Douglas; Sarhangi, Reza (eds.). Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture. Phoenix, Arizona, USA: Tessellations Publishing. pp. 637–642. ISBN 978-1-938664-00-7. ISSN 1099-6702. Retrieved 10 July 2015.