Zero-dimensional space

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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 zero-dimensional space is a point. [2]

Contents

Definition

Specifically:

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

Properties of spaces with small inductive dimension zero

Manifolds

All points of a zero-dimensional manifold are isolated.

Notes

References

  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. Archived from the original (PDF) on 26 June 2015. Retrieved 10 July 2015.