DefinitionIn other words, homeomorphisms are bicontinuous functions between topological spaces. Its preserves the topology of spaces, like for example, connectedness, compactness. A second type of structure, the classification of spaces according to their shape, that is, according to the homeomorphisms, by which we learn itself is called the topology. If they are homeomorphic to each other -we say it more informally that these are topologically equivalent two spaces. For an example, the function f(x) = x3 is a homeomorphism of the real line R onto itself: it is continuous and bijective, and its inverse is also continuous.
