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Topological_space_examples.svg‎ (SVG file, nominally 360 × 319 pixels, file size: 12 KB)

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Description	Topological space examples.svg 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)
Date	25 May 2008(2008-05-25)
Source	Own work
Author	Dcoetzee
Permission (Reusing this image)	See below.

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	06:54, 26 May 2008		360×319 (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 )