In topology and related areas of mathematics a topological property or topological invariant is a property of a topological space which is invariant under homeomorphisms. That is, a property of spaces is a topological property if whenever a space X possesses that property every space homeomorphic to X possesses that property. Informally, a topological property is a property of the space that can be expressed using open sets.
A common problem in topology is to decide whether two topological spaces are homeomorphic or not. To prove that two spaces are not homeomorphic, it is sufficient to find a topological property which is not shared by them.
Famous quotes containing the word property:
“I would gladly chastise those who represent things as different from what they are. Those who steal property or make counterfeit money are punished, and those ought to be still more severely dealt with who steal away or falsify the good name of a prince.”
—Elizabeth I (1533–1603)