Is an original refinement of a theorem eligible to be published on some journal? 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 &quot;that one&quot; with too much self-esteem). Thanks in advance!
Generally, an extension of a theorem is valuable. But whether it is publishable is up to a publisher. The way they make a decision is to have submissions reviewed by experts. But you can, in most cases, also seek expert help in evaluating the work you do. As suggested in the comments, local professors might be good for that.
But you can just write it up and submit it. To find an appropriate journal, you need to find a few candidates and, at least, look at the index to see what sorts of things they publish.
However, it may be that your work would be considered a trivial extension rather than something with value. That would hinge on one or both of two things. First, the theorem statement itself might provide insights into understanding topological spaces. But, and probably more important, the form of the proof you provide might provide insight into the solution of other problems. Often the proof is more important than the theorem itself. Your suggestion that you needed additional lemmas to extend an old proof might be your key to success.
If/when you submit you will get feedback on the work and possibly suggestions to improve it. But it takes reading of the paper to decide on its value.