I am a self-learner. What background knowledge is necessary to learn Analysis and Topology?
Calculus, an experience with proofs and an experience with sets.
Personally, I would take analysis before you take topology. Make sure you know about metric spaces before topology (metric spaces are usually studied in analysis, but not always).
If you studied calculus from a rigorous book like Spivak, then you can take on a rigorous analysis book (like the excellent book by Aliprantis & Burkinshaw). Otherwise, the book "Understanding Analysis" by Abbott is very good.
Is it weird that my school's real analysis is a course on topology and metric space? I'm only first year but that's what my calculus teacher told me when i asked what real analysis was. He told me the course content for real analysis course at my school was metric space and topology.
I keep on hearing about "reconstruction" of the real numbers... but apparnetly that's done in abstract algebra and or set theory 3rd year course. Is this normal?
That's a bit weird. Metric spaces (and a little topology) are certainly part of real analysis, but real analysis should be much more then that. It should also deal with differentiation, integrals, series, etc. It's a bit weird if you only see topology in your real analysis course.
Reconstruction of the real numbers is very often done in real analysis, because it's important to know what the real numbers are exactly. It is extremely weird that you do this in abstract algebra, I never heard of such a thing before. It would fit in a set theory course though.
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