Read Introduction to Topology by Bert Mendelson Free Online
Book Title: Introduction to Topology|
The author of the book: Bert Mendelson
Edition: Dover Publications
Date of issue: July 1st 1990
Format files: PDF
The size of the: 546 KB
City - Country: No data
ISBN 13: 9780486663524
Loaded: 2855 times
Reader ratings: 6.7
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I'm not yet enough of an expert on topology to give this a truly informed review; I can compare this to only to one other topology text (but plenty of math books).
The book starts out with a very compact review of set theory (no pun intended). Then comes a warmup chapter on metric spaces, which seems a bit cumbersome in places, but is turns out to be carefully designed to use exactly the same structure as will be used when introducing similar topics for topological spaces. The tour through metric spaces is quite helpful, introducing abstract definitions of topics such as continuity, neighborhoods and limit points that are crucial in topological spaces while the reader still has the crutch of distances to fall back on to make sense of the concepts. The topology content covered is entirely point-set topology, covering the basics of openness, compactness, and connectedness, without moving any deeper.
The book is very self-contained, and should be accessible to any undergrad comfortable with proofs and preferably at least some exposure to real analysis. That's not to say reading it is simple, however; expect to put in some work following the proofs and solving problems if you want to get something out of it.
The style of the book is quite elegant and spare. It doesn't elaborate once an argument or proof is complete, but is quite readable despite its terseness. This style will be too brief for students who want more redundancy, hand-holding, and worked exercises. But it's quite enjoyable for those who are willing and able to supply the mental effort and let the author guide your efforts. The book includes plenty of end-of-section examples, of a range of difficulties. Working a sampling of these after each section is plenty to ensure that you have understood the material. One thing I would have appreciated, though, is a few more examples of non-Euclidean topological spaces that I could have used as exercises to poke at the definitions and proofs. My intuition is still embedded way too deeply in Euclidean space, and I have to stress-test it to know when I'm relying on it too much.
Some of the terminology used is slightly non-standard, or out-of-date. The theorems never change, but the wording does, slowly, and this is visible when Mendelson uses terms like identification topology rather than quotient space. This makes it slightly more inconvenient to match topics when supplementing this text with other sources or vice versa, but I suppose this is inevitable in a book that was first published more than 50 years ago. Texts in fields other than math tend to become dated much faster.
The best part about the book is the price. Dover editions are nearly always a bargain, and this one is no exception. It almost seems like it should be illegal to get this much good stuff for $10.95.
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