A mathematical topology is a set ''X'', and a collection ''tau'', of subsets of ''X'', called ''OpenSets'', satisfying the following 3 conditions:

	1. ''X'' and the empty set are in ''tau''.
	1. If any two subsets of ''X'' are in ''tau'', so is their intersection.
	1. If any family of subsets of ''X'' are in ''tau'', so is their union.

Such a set, ''X'', may be referred to as a topological space.
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Use this page now: http://planetmath.org/encyclopedia/TopologicalSpace.html. -- JohnHarby

''And I learned from this definition, so that makes it on topic - that's why I visit.'' -- jimrussell
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They don't have to be weird doughnuts either. 2 simple examples:

	1. The class of all SubSet''''''s of X (PowerSet) is a topology on X called the Discrete topology
	2. The class consisting of just X and {} (empty set) alone is called the Indiscrete topology
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CategoryMath