You don't really need to go through a set theory book. Munkres is self-contained and introduces everything you need. Apart from the standard set theoretical operations, you won't need much set theory? So you need to know very well things like
A⊆f−1(f(A))
Other references include: the standard in the old days was Halmos's Naive set theory. I liked Erich Kamke's book too.
Set theory is a branch of mathematics that deals with the study of sets, which are collections of distinct objects. Topology is a branch of mathematics that deals with the study of spaces and their properties. Set theory is the foundation of topology, as it provides the tools and concepts needed to define and analyze topological spaces.
The basic concepts of set theory include sets, elements, subsets, union, intersection, and complement. The basic concepts of topology include open sets, closed sets, neighborhoods, continuity, and compactness.
A set theory book for topology focuses on the use of set theory to understand and analyze topological spaces. It may also cover topics such as cardinality, ordinals, and transfinite numbers, which are important in topology. Other books on topology may focus more on the geometric and topological properties of spaces.
Set theory is used in topology to define and study topological spaces, which have many practical applications in fields such as physics, engineering, computer science, and economics. For example, topological spaces are used to model networks, analyze data, and design algorithms.
Some recommended set theory books for topology include "Topology" by Munkres, "Introduction to Topology: Pure and Applied" by Adams and Franzosa, and "General Topology" by Kelley. These books provide a thorough introduction to set theory and its applications in topology, suitable for both beginners and advanced learners.