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:
“You and I ... are convinced of the fact that if our Government in Washington and in a majority of the States should revert to the control of those who frankly put property ahead of human beings instead of working for human beings under a system of government which recognizes property, the nation as a whole would again be in a bad situation.”
—Franklin D. Roosevelt (1882–1945)