This book was written to be [a readable introduction
(to algebraic topology) (with rather broad coverage of the subject).]
の to be 以後の名詞句のうち、主要部を取りだしてきただけだと思うけど。

なんでそれだけでto不定詞の用法を分かってないことになるのかいみふ
this book も was も written も to algebraic topology も
with rather broad coverage of the subject も省略してあるのに