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One could study basic topology if he/she has a good understanding of calculus (single variable & multi variable) and linear algebra. Basic concepts in topology can be understood by this set of prerequisites.

Functional analysis is a lot of topology and does need calculus. But to start with the basic concepts of topology, you will only need to know what a set is - and the empty set. That's all you need to get started.

Technically Munkres' Topology has no formal prerequisites, but it's a rough go of it if you haven't had a rigorous exposure to continuity and metric spaces already. The second part of the book also assumes knowledge of elementary abstract algebra.

Technically Munkres' Topology has no formal prerequisites, but it's a rough go of it if you haven't had a rigorous exposure to continuity and metric spaces already. The second part of the book also assumes knowledge of elementary abstract algebra.

The prerequisite is linear algebra together with an introduction to proofs. However, a more advanced version of this course could be taught with a prerequisite of a one-semester course in undergraduate analysis.

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