Prove the following: theorem: every topological group iscompletely regular. Proof. Let V0 be a neighborhood of the identityelemetn e, in the topological group G. In general, coose Vn to be aneighborhood of e such that Vn.VncVn-1. Consider the set of alldyadic rationals p, that is all ratinal number of the form k/sn,with k and n inegers. FOr each dyadic rational p in (0,1], definean open set U(p) inductively as foloows: U(1)=V0 and
