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1-"Introduction to the Representation Theory

1-"The structure of Compact and Locally Compact Groups 1983compact groups 2006" written by"Alain Robertby"Karl Heinrich Hofmann, Sidney A. Morris"

2-"Representations of Finite and Compact Groups 1995" written by"Barry Simon"

3-"The structure

3-"Introduction to the Representation Theory of compact groups 2006Compact and Locally Compact Groups 1983" written by"Karl Heinrich Hofmann, Sidney A. Morrisby"Alain Robert"

But for what you want "... in metric topological ..." I suggest you try to getting reach to Professor "S. Mohammad Tabatabaie" (about his family the spelling perhaps be different but pronunciation is correct) who his field is Harmonic Analysis and is in Qom University.
show/hide this revision's text 2 added 371 characters in body

1-"Introduction to the Representation Theory of Compact and Locally Compact Groups 1983" written by"Alain Robert"

2-"Representations of Finite and Compact Groups 1995" written by"Barry Simon"

3-"The structure of compact groups 2006" written by"Karl Heinrich Hofmann, Sidney A. Morris"

But for what you want "... in metric topological ..." I suggest you try to getting reach to Professor "S. Mohammad Tabatabaie" (about his family the spelling perhaps be different but pronunciation is correct) who his field is Harmonic Analysis and is in Qom University.
show/hide this revision's text 1

1-"Introduction to the Representation Theory of Compact and Locally Compact Groups 1983" written by"Alain Robert" 2-"Representations of Finite and Compact Groups 1995" written by"Barry Simon"