A mathematical topology is a set
X, and a collection
tau, of subsets of
X, called
OpenSets, satisfying the following 3 conditions:
- X and the empty set are in tau.
- If any two subsets of X are in tau, so is their intersection.
- 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.
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
They don't have to be weird doughnuts either. 2 simple examples:
- The class of all SubSet?s of X (PowerSet) is a topology on X called the Discrete topology
- The class consisting of just X and {} (empty set) alone is called the Indiscrete topology
CategoryMath