- #1

Math Amateur

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I need help with some aspects of the proof of Proposition 2.1.4 ...

Proposition 2.1.4 and its proof read as follows:View attachment 8039

In the above proof by Paul Bland we read the following:

" ... ... Since \(\displaystyle p_\alpha u_\alpha = \text{ id}_{ M_\alpha }\), we have that \(\displaystyle u_\alpha\) is an injective mapping and that \(\displaystyle p_\alpha\) is surjective ... ... "Can someone please explain exactly how/why \(\displaystyle u_\alpha\) is an injective mapping ... ?Help will be appreciated ...

Peter