Zero-dimensional space

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This article is about zero dimension in topology. For several kinds of zero space in algebra, see zero object (algebra).

In mathematics, a zero-dimensional topological space (or nildimensional) 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][2] An illustration of a nildimensional space is a point.[3]

Definition[edit]

Specifically:

The two notions above agree for separable, metrisable spaces.

Properties of spaces with covering dimension zero[edit]

Notes[edit]

References[edit]

  1. ^ "zero dimensional". planetmath.org. Retrieved 2015-06-06. 
  2. ^ Hazewinkel, Michiel (1989). Encyclopaedia of Mathematics, Volume 3. Kluwer Academic Publishers. p. 190. 
  3. ^ Wolcott, Luke; McTernan, Elizabeth (2012). "Imagining Negative-Dimensional Space" (PDF). In Bosch, Robert; McKenna, Douglas; Sarhangi, Reza. 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.