3,4) and TY = Y defined by f(a)=4, f(b) defined by g(a) = 1, g(b)=g(c)=3 and g(d) = 4. Then * Let X= (a, b, C, d} and TX = (Ø, X, {b}, (b,c}, {a,b,d}} be a topology on X. Let Y= {1, 2. (Ø, Y, (3),...

Extracted text: 3,4) and TY = Y defined by f(a)=4, f(b) defined by g(a) = 1, g(b)=g(c)=3 and g(d) = 4. Then * Let X= (a, b, C, d} and TX = (Ø, X, {b}, (b,c}, {a,b,d}} be a topology on X. Let Y= {1, 2. (Ø, Y, (3), (1,2,3}} be a topology on Y. Let f be a mapping from X into = 4. Let g be mapping from X into Y = 3, f(c) = 2 and f(d) %3D f and g are not continuous O fis continuous and g is not continuous f is not continuous and g is continuous O fand g are both continuous A property is said to be a topological property if it is preserved by homeomorphism. Suppose that R is equipped with the usual topology, then the boundedness and the closedness are not topological properties because* O la.b] is not homeomorphic to Ja.bl O Ris homeomorphic to1, O[ earch TOSHIBA