To give an imperfect programming language analogy, imagine that every symbol is implicitly defined and has lexical scope. The grammar is as far from being context-free as possible. What may sometimes look like individual symbols to you are in fact a collection of inseparable symbols with its own semantic parse.
A resource that would explain formal mathematical notation would be great, much like a dictionary.
You can't google those symbols properly either.
I don't think the symbols are the problem. They're a very superficial obstacle, at least in this paper.
This isn't meant as a put-down. It's just that I really do think the actual material requires a lot more preparation that consists in a lot more than just learning the definition of the symbols. I could rewrite the whole paper using only text and no symbols. The symbols are just shorthand for English words. I don't think if I were to replace all of the symbols with the English words that they stand for, you would be much closer to understanding.
OK, so then why would it be so difficult to produce a veritable cheat sheet to aide in reading a proof?
Anyway are symbols really the main obstacle for you? When you read "every second countable regular Hausdorff space is metrizable" (theorem 59 in this paper), you have no problem understanding what this means?
And then I'd have to explain the words I used to explain these words.
It all just takes a while. I might be able to do it, but we'd both need to spend some time understanding all of this together, going back and forth, considering examples, and building the foundations.