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  3. prove the following: theorem: every topological gr

Prove the following: theorem: every topological group is completely regular. Proof. Let V0 be a neighborhood...

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Advance Math

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

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