Topological Space

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.
2. If any two subsets of X are in tau, so is their intersection.
3. 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 SubSets 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