Let f be a map from T 1 into S and g be a map from T 2 into S . Let S , T be non empty topological spaces. One can verify that there exists a map from S into T which is continuous. One can prove the following proposition For all non empty topological spaces S , T holds every continuous mapping from S into T is a continuous map from S into T . Let T be a non empty topological structure.
T is open and continuous.
Let T be a non empty topological structure. We now state the proposition Let S , T be non empty topological spaces and f be a map from S into T . If f is a homeomorphism, then f -1 is open.