- Proof: "any topological space with the fixed point property is connected" - PlanetMath
Theorem Any topological space with the fixed-point property is connected. Proof. We will prove the contrapositive. ....
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Note: A decent explanation of the fixed point property: http://planetmath.org/encyclopedia/FixedPointProperty.html
- FreeMind - Wikipedia, the free encyclopedia
FreeMind is a free mind mapping application written in Java. FreeMind is licensed under the GNU General Public License. Along with the advantage of unlimited free usage, it provides extensive export capabilities. An XHTML export allows you to create a mapped image with links to a folding outline. Natara Software's Bonsai outliner also allows you to import the mindmap into a hierarchical list, thereby allowing you to easily carry around your maps (in outline form) on your Palm PDA.
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- Mind mapping, concept mapping and information organisation software
Vic's compendium of software that supports knowledge management and information organisation in graphical form. Includes mind mappers, concept mappers, outliners, hierarchical organisers, KM support and knowledge browsers, 2D and 3D. The opinions are Vic's but material in quotes that follows "What they say" is quoted from the vendors' web sites. All prices are as at the most recent update (March 06). "$" means US dollars
Mindmapping software, concept mapping software, information organisation software
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- Separation axiom - Wikipedia
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are axioms only in the sense that, when defining the notion of topological space, you could add these conditions as extra axioms to get a more restricted notion of what a topological space is. The modern approach is to fix once and for all the axiomatization of topological space and then speak of kinds of topological spaces.
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Note: See also: The precise meanings of the terms associated with the separation axioms has varied over time, as explained in History of the separation axioms... http://en.wikipedia.org/wiki/History_of_the_separation_axioms
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