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 nildimensional 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.

Hypersphere

The zero-dimensional hypersphere (0-sphere) is a pair of points, and the zero-dimensional ball is a single point. [3]

Notes

Related Research Articles

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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 . Retrieved 10 July 2015.
  3. Gibilisco, Stan (1983). Understanding Einstein's Theories of Relativity: Man's New Perspective on the Cosmos. TAB Books. p. 89. ISBN   9780486266596.