Topological space

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Consider to be a non-empty set, and also let be a subset of the power set of , such that an action fullfils the following conditions,

  • ,
  • if then also the finite intersetion of these sets are element of the topology, i.e.
  • let be an index set and for all the subset is element of the topology () then also the union of these sets is an element of the topology <\math>, i.e.

The pair is called topological space. Set sets in are called the open sets in .

Learning Task

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  • Let and . Add a minimal number of sets, so and create , so that is a topological space.