Image:Topological space examples.svg

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[edit] Summary

Description

Examples and non-examples of topological spaces, based roughly on Figures 12.1 and 12.2 from Munkres' Introduction to Topology. The 6 examples are subsets of the power set of {1,2,3}, with the small circle in the upper left of each denoting the empty set, and in reading order they are:

  • {{}, {1,2,3}} (the trivial topology)
  • {{}, {1}, {1,2,3}}
  • {{}, {1}, {2}, {1,2}, {1,2,3}}
  • {{}, {2}, {1,2}, {2,3}, {1,2,3}}
  • {{}, {2}, {3}, {1,2,3}} (not a topology, because {2} and {3} are in the topology but their union {2,3} is not)
  • {{}, {1,2}, {2,3}, {1,2,3}} (not a topology, because {1,2} and {2,3} are in the topology but their intersection {2} is not)
Source

self-made
Date

May 25, 2008.
Author

Dcoetzee
Permission
(Reusing this image)

see below

[edit] Licensing:

Public domain I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Date/TimeDimensionsUserComment
current06:54, 26 May 2008360×319 (12 KB)Dcoetzee ({{Information |Description=Examples and non-examples of topological spaces, based roughly on Figures 12.1 and 12.2 from Munkres' ''Introduction to Topology''. The 6 examples are subsets of the power set of {1,2,3}, with the small circle in the upper left )
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