To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Zero-dimensional space

From Wikipedia, the free encyclopedia

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]

YouTube Encyclopedic

  • 1/5
    Views:
    592 366
    531
    378
    906 967
    2 007 323
  • Imagining the "Zeroth" Dimension
  • Geometry Lecture1(ZERO DIMENSION / NO DIMENSION,ONE DIMENSION)
  • The Illusion of Space
  • The Mathematics of our Universe
  • Visualizing quaternions (4d numbers) with stereographic projection

Transcription

Definition

Specifically:

  • A topological space is zero-dimensional with respect to the Lebesgue covering dimension if every open cover of the space has a refinement which is a cover by disjoint open sets.
  • A topological space is zero-dimensional with respect to the finite-to-finite covering dimension if every finite open cover of the space has a refinement that is a finite open cover such that any point in the space is contained in exactly one open set of this refinement.
  • A topological space is zero-dimensional with respect to the small inductive dimension if it has a base consisting of clopen sets.

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

  • Arhangel'skii, Alexander; Tkachenko, Mikhail (2008). Topological Groups and Related Structures. Atlantis Studies in Mathematics. Vol. 1. Atlantis Press. ISBN 978-90-78677-06-2.
  • Engelking, Ryszard (1977). General Topology. PWN, Warsaw.
  • Willard, Stephen (2004). General Topology. Dover Publications. ISBN 0-486-43479-6.

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.
This page was last edited on 3 January 2024, at 18:15
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.