One can verify that Cl D is lower bounded. Let D be an upper bounded subset of . One can check that Cl D is upper bounded. Let us observe that REAL 1 is T 2 . B be a subset of REAL 1 .
B is compact.
Let us note that every subset of which is finite is also compact. Let a , b be real number. Let us note that there exists a subset of which is non empty, finite, and bounded. Let T be a topological structure, f be a RealMap of T , and g be a map from T into REAL 1 .