In this note we observe that epimorphisms in the category of C~*-algebras are surjective and thus answer a question raised by V. G. Pestov in the affirmative [3]. To show this claim it clearly suffices to prove that epimorphically embedded subalgebras cannot be proper, and this is what we shall verify. The word subalgebra will always mean C~*-algebra. For a C~*-algebra A let Ah denote the closed vector subspace of hermitian elements of A.
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机译：在本说明中，我们观察到C〜*代数范畴内的同胚是排斥性的，因此回答了V. G. Pestov提出的肯定性问题[3]。为了证明这一点，显然足以证明表面上嵌入的子代数是不正确的，这就是我们将要验证的。子代数一词始终表示C〜*-代数。对于C〜*代数A，让Ah表示A的埃尔米特元素的封闭向量子空间。
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