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Monday, June 18, 2007


Let X be any set and let T be a family of subsets of X. Then T is a topology on X if
- both the empty set and X are elements of T,
- any union of elements of T is an element of T, and
- any intersection of finitely many elements of T is an element of T.
If T is a topology on X, then X together with T is called a topological space.

X = {a,b,c} is a set.
T = {0, {a,b,c}, {a,b}, {a,c}, {b,c}. {a}, {b}, {c} } is a family of subsets.
[X, T] is a topological space.

From "Topology Without Tears" by

Sidney A. Morris.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)