I am an undergraduate student majoring in math and economics and I managed to prove a theorem (10 page long theorem) that was only stated for functions in the real line with valures in the real line, and I generalized the whole (pretty convoluted structure) to a general topological space. The proof is pretty the same, but what I am showing is that all the passages can be done and my original contribution is to justify all the passages that in the real line were for free, while in a general topological space they needed at least 2 or 3 intermediate lemmas that actually account for 3/4 pages of original proofs. Working it all with the nitty gritty details, the whole paper becomes 30/40 pages long (with intro and related literature, proof, lemmas and conclusion).
My question is the following: My field is mathematical economics. How can I be sure my generalization can be submitted to some academic journal? I am sure no one has ever done it before but I do not know how important my contribution can be. Probably it is not worth to be published in Econometrica or Journal of Economic Theory (two of the best econ journals), but I am asking here:
- How can I understand if my generalization deserves at least a try to some medium/low-rank journal?
- How can I understand which journal best fits my work?
Please, do not answer referring me to some professors in my department, since I would rather not risk to go to their office and feel ashamed to have proposed a work that actually is not worth publishing (I mean, I do not want to be "that one" with too much self-esteem). Thanks in advance!