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My manuscript (currently freely available on the Web) was rejected by a publisher. They essentially say my theory is unmotivated. (In my own opinion my research is motivated for example as a tool to study less general spaces such as proximity spaces, and by internal beautify of the formulas in my theory.)
Could you look into my manuscript and express your opinion whether you’d agree to publish my work?
Which publisher to send it to?
I didn’t read any of it to see what the mathematical content is, but if they say it is “unmotivated” I assume they mean that there is no exposition. Even in short papers there needs to be a lot more than just definitions, statements, and proofs. In a work as long as this, lots of exposition becomes even more important.
You can have good mathematics and good motivation, but if there is nothing to guide the reader in understanding what you are doing and why, then it won’t get across. Just take Chapter 2 for example. It only contains a couple (maybe 2?) sentences that would qualify as exposition.
Even in something like Jacob Lurie’s Higher Algebra which has a similar approach to you with labeling everything into a rigorous definition, statement, proof, example, remark, etc format begins with lots of motivating problems and examples. Each section begins with exposition about what is going to happen in the section and why it fits into the overall plan of the book and so on.
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