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(Nonfiction: Topological space: Four examples and two non-examples of topologies on the three-point set {1,2,3}. The bottom-left example is not a topology because the union of {2} and {3} [i.e. {2,3}] is missing; the b...)
 
 
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Nonfiction: [[Topological space (nonfiction)|Topological space]]: Four examples and two non-examples of topologies on the three-point set {1,2,3}. The bottom-left example is not a topology because the union of {2} and {3} [i.e. {2,3}] is missing; the bottom-right example is not a topology because the intersection of {1,2} and {2,3} [i.e. {2}], is missing.
Nonfiction: [[Topological space (nonfiction)|Topological space]]: Four examples and two non-examples of topologies on the three-point set {1,2,3}. The bottom-left example is not a topology because the union of {2} and {3} [i.e. {2,3}] is missing; the bottom-right example is not a topology because the intersection of {1,2} and {2,3} [i.e. {2}], is missing.
In [[Topology (nonfiction)|topology]] and related branches of [[Mathematics (nonfiction)|mathematics]], a '''topological space''' may be defined as a set of points, along with a set of neighborhoods for each point, satisfying a set of axioms relating points and neighborhoods.
The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence.
Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints.
Being so general, topological spaces are a central unifying notion and appear in virtually every branch of modern mathematics.
The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.


== In the News ==
== In the News ==


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File:Mug and Torus morph.gif|link=Topology (nonfiction)|[[Topology (nonfiction)|Topology]] lesson says it "never gets tired of changing from a cup to a donut and back again."
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== Nonfiction cross-reference ==
== Nonfiction cross-reference ==


* [[Axiom (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Mathematics (nonfiction)]]
* [[Topology (nonfiction)]]
* [[Topology (nonfiction)]]
* [[Topological space (nonfiction)]]


External links:
External links:

Latest revision as of 11:32, 6 August 2017

Nonfiction: Topological space: Four examples and two non-examples of topologies on the three-point set {1,2,3}. The bottom-left example is not a topology because the union of {2} and {3} [i.e. {2,3}] is missing; the bottom-right example is not a topology because the intersection of {1,2} and {2,3} [i.e. {2}], is missing.

In the News

  • Topology lesson says it "never gets tired of changing from a cup to a donut and back again."

    Topology lesson says it "never gets tired of changing from a cup to a donut and back again."

Fiction cross-reference

Nonfiction cross-reference

External links:

Attribution:

By Dcoetzee - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=4114048

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