I have the function (a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})" alt="f(a,b),U_{(a,b)})\rightarrow((c,d),U_{(c,d)})" />, where is the subspace topology of the usual topology where A = (a,b) and is the subspace topology of the usual topology where A = (c,d), defined as

How do I show this function is continuous?