- File Size: 460081 KB
- Print Length: 537 pages
- Publication Date: February 27, 2018
- Sold by: Amazon.com Services LLC
- Language: English
- ASIN: B07B4J84KG
- Text-to-Speech: Enabled
- Word Wise: Not Enabled
- Lending: Not Enabled
- Amazon Best Sellers Rank: #1,276,611 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
Topology: Pearson New International Edition Kindle Edition
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This text is excellent for self study assuming you've taken an analysis course and followed the proofs enough to do reasonably well in the exercises (when you screwed up-you figured out why.). General or point set topology is essentially math analysis distilled to its basic constructs and arguments (proof forms). Great theorems in analysis become great ideas in general topology. One theorem I've oft repeated is that a metric space is compact if and only if every infinite sequence (in it) has a limit point(in it)-or point of accumulation-this theorem is the prototype for the notion of sequential compactness. You'll see arguments from analysis repeated or called upon throughout-same friends just different clothes on them.
Even though this is an introduction I still look up proofs in it for things like the Tietze extension theorem, the Stone–Čech compactification, and the compact-open topology. A book at one level higher, which has material not contained in Munkres, is Willard, General Topology (Dover Books on Mathematics). An example of a theorem that is proved in Willard but not Munkres is that a product of *continuum* many Hausdorff spaces each with at least two points is separable if and only if each factor is separable (Theorem 16.4 in Willard). Willard is also better for the topology of function spaces. But Munkres is much easier to learn from and Munkres should always be used rather than Willard for a first course.
Additionally, I found the problems just a joy to work. They were very good at developing and then building understanding.
The second part of the book approaches algebraic toplogy, which is still tangeable.
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Davvero ben fatto
Also, it seems that the book is not allowed to sell outside India subcontinent.
Note: Dont skip chapter 1