I am a graduated student in physics, and interested on topological properties of the matter, as it is a really hot topic. In physics, the topological properties arise from symmetries in the models. However, I have the feeling that I don't fully understand why topology is so important in a mathematical context. So, I would like to know more about this topic from a mathematical point of view. Is there any introductory reference that I could use for learning it? My mathematical background is similar to a first course in mathematical diploma. Thank you for any suggestion!
2026-03-31 17:49:11.1774979351
Book suggestion: An introduction for topology
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One of the better known texts on introductory topology is Topology by James Munkres. You find the second edition online for free via google (I'd put the link put I'm not sure it's technically in the public domain.)
Two book I would recommend in addition to Munkres are Introduction to Metric and Topological Spaces by Sutherland and Introduction to Topology: Pure and Applied by Colin Adams and Robert Franzosa.
The book mentioned by Carry on Smiling in the comments section is also said to be good by many and you can get it for free as well. Here is the link for Topology without Tears: http://www.topologywithouttears.net/topbookprint.pdf But you simply can't open the file without a pass key but you can easily get it, I hear, from the author.
Hope you found this helpful and good luck!