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I am an undergraduate student of Mathematics and I want to study the topic "Separation Axioms" of general topology.I have already studied Basis,Subbasis,Product topology,Countability axioms,sequences and continuous functions.I tried to study Munkres but it is not suitable for me.I am looking for a text where the topics $T_1,T_2,T_3,T_{3\frac{1}{2}},T_4$,Urysohn's Lemma,Tietze extension theorem are discussed in detail.Can someone help me find such a text or note?I am a beginner,so I also need some motivation behind this chapter.

Kishalay Sarkar
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    What specifically is not suitable about Munkres? – Eric Wofsey Jul 17 '21 at 04:33
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    Did you check the articles separation axioms and Axiomes de séoaration on Wikipedia? They both contain several references. – J.-E. Pin Jul 17 '21 at 04:55
  • Seperation Axioms? There are like 20 of them and every author numerates them differently... – Cornman Jul 17 '21 at 05:02
  • I second the recommendation to look into the wikipedia page on Separation axioms. I learned topology from Munkres, and he doesn't quite cover enough (perhaps some things were not known to him at the time he authored that text that are known now?), in particular Pre-Regular spaces are important to understanding the overall relationship between many of the separation axioms (something that was not known until much later into the 20th century). – Justin Benfield Jul 17 '21 at 05:16
  • Could you be more specific about why Munkres is not suitable for you? You say you're a beginner, and Munkres is generally the recommended text for beginners (as opposed to Kelly, Dugundji, Wilansky, Gaal, Cullen, Engelking, Willard, etc. that are pitched at a slightly higher level) that would cover the topics you want to focus on. Maybe some of the texts mentioned in this answer, although note that the OP there wanted a book to supplement a similar such text that includes some homotopy theory (but also see the comments there). – Dave L. Renfro Jul 17 '21 at 06:39

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There are two important books. The book of James Dugundji Topology and the book of Willard. Also, for a basic introduction, you can read "An Introduction to General Topology", Paul E. Long (not available online)

Mohammad W. Alomari
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A standard reference work that covers all those topics, and many more, is Engelking's book "General Topology" (2nd ed 1989). Many topology papers use it as the default reference for all standard facts.

Henno Brandsma
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