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R.P.F.
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Hi! Can someone recommend some books on point set topology for undergraduates? I am going to use it this summer for preview and also during the fall because the instructor is not going to use a textbook. Thank you!
micromass said:Hi R.P.F.!
I can highly recommend Munkres! It's one of the best topology books out there. It's really made for somebody's first encounter with topology. It doesn't only explain things in a lot of details, but it also goes quite deep into the topology!
Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach. It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. If you ever start wondering if there exists a separable compact space that is not connected? Check this book and find out!
My favorite topology book is "General topology" of Willard. But I wouldn't recommend it to beginning students. It might be a bit dense...
Point set topology is a branch of mathematics that studies the geometric properties of sets of points in a space, without considering the specific shape or size of the points. It is concerned with topological spaces, which are mathematical structures that describe the relationships and properties of points within a given set.
Books on point set topology are important because they provide a comprehensive and rigorous introduction to this fundamental branch of mathematics. They cover the key concepts, theorems, and techniques used in point set topology, and can be used as a reference for further study or research.
Books on point set topology typically cover topics such as topological spaces, continuity, connectedness, compactness, and separation properties. They also introduce more advanced concepts, such as homotopy, homology, and cohomology, and their applications in various fields of mathematics and science.
Books on point set topology can benefit anyone interested in mathematics, physics, computer science, or any other field that involves the study of geometric structures. They are particularly useful for graduate students and researchers who want to deepen their understanding of topology and its applications.
A basic understanding of real analysis and set theory is usually required to fully understand books on point set topology. Some books may also assume knowledge of abstract algebra or differential geometry. It is recommended to check the prerequisites before starting a specific book on point set topology.