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Proof. To verify F pS,Gq forms a group with this operation, we must check the existence of an identity element, the existence of inverses, and associativity. The identity element for F pS,Gq will beContinue Reading
Proposition 3. Q is not open nor is RzQ. Proof. The rationals and irrationals are dense in R. Hence, for any x P Q, Bδpxq must contain an element in RzQ for all δ ą 0, and therefore Q is not open.Continue Reading