A property is said to be a topological property if it is preserved by homeomorphism. Suppose that Ris equipped with the usual topology, then the boundedness and the closedness are not topological...

Topology


Extracted text: A property is said to be a topological property if it is preserved by homeomorphism. Suppose that Ris equipped with the usual topology, then the boundedness and the closedness are not topological properties because * [0,1] is not homeomorphic to ]0,1[ R is homeomorphic to ]0,1[ R is homeomorphic to ]0, +o[ O 1-00,0] is homeomorphic to [0,+o[