III4 Alpha Complexes. Computational Algebraic Topology. IV2 Matrix Reduction. IV3 Relative Homology. IV4 Exact Sequences. V3 Intersection Theory. V4 Alexander Duality. VII2 Efficient Implementations.
VII3 Extended Persistence. VII4 Spectral Sequences. IX2 Elevation for Protein Docking. IX3 Persistence for Image Segmentation. IX4 Homology for Root Architectures. Morse Functions. VI4 Reeb Graphs.
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Community Reviews. Showing Rating details. More filters. Sort order. Sep 14, Steve Stuart rated it really liked it.
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 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 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.
Sep 06, CD rated it really liked it Shelves: mathematics , reference , textbook. I actually have the Second Edition, must speak with a librarian or become one to add this and several other 'older' books of this standard.
Not unlike several other 'Intro' books, there is a rather large amount of pre-req knowledge required. If you are firmly rooted in your understanding of Set Theory and have had rigorous levels of experience with that nomenclature, only the first couple of readings will be a muddle.
One of the best formal introductions to basic Topology. If you are studying a I actually have the Second Edition, must speak with a librarian or become one to add this and several other 'older' books of this standard. If you are studying any of the modern flashback theories of the universe, the relationship between Hilbert Space and Euclidean inclusion along convergences is a must! A little dense initially on the important topic of convergence, but you will get there more quickly than with most other elaborations that I know of up to books even as recent as years ago circa This is basic stuff folks!
Get it right the first time and your wonderment over dimensionality will become a diminishing metric subspace oops, another obscure application of Topology and not intro level. View 1 comment. Jun 02, Billy Dean rated it liked it. You caught me--technically, I haven't finished this book yet. I'll admit that I'm not quite ready to tackle topology itself.
Mathematics – Introduction to Topology. Winter Closed Sets (in a metric space). While we can and will define a closed sets by using the definition. This book provides a concise introduction to topology and is necessary for courses in differential geometry, functional analysis, algebraic topology, etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of.
However, the introductory overview of set theory and set theoretical notation is invaluable if you're interested at all in foundational mathematics or philosophy of mathematics be it Russell or Badiou. I had worn myself out on other books dedicated to the subject, and this book provides a clearer, more to-the-point account of basic set theory than any I've found in a fi You caught me--technically, I haven't finished this book yet. I had worn myself out on other books dedicated to the subject, and this book provides a clearer, more to-the-point account of basic set theory than any I've found in a fifty page introduction, no less!
Algebraic topology is a branch of mathematics that uses tools from algebra to study topological spaces. Libraries and resellers, please contact cust-serv ams. From Wikipedia, the free encyclopedia. Topology is relevant to physics in areas such as condensed matter physics ,  quantum field theory and physical cosmology. Heitzig, J. The words nearby , arbitrarily small , and far apart can all be made precise by using open sets.
In this regard, it's worth the read. I'll get back to you about the rest when I'm more prepared to treat topology in earnest. Jul 11, Jason Evans rated it liked it. Good lord I hate topology.
Good book on it, though. Aug 14, Chandra Prakash rated it really liked it. This is my first book on Topology, and it's quite good. First few chapters are basic and about sets, functions. The nest thing I liked about this book was that it connected the topics connectedness to intermediate value theorem and as such. It was sort of helpful in getting the big picture of Topology and its relationship to calculus and other branch of Mathematics.
Great Book to start studying Topology. Jun 28, Simona Vesela rated it it was amazing Shelves: mathematics. It has taken me roughly 20 hours to read the first 40 pages. That was 4 years ago. Last few weeks I have worked through the rest in maybe 10 hours.