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A great companion to Munkres to have.[Review 1 - 05/05/17.]
Pretty perfect maths book. Does what it says on the tin. One thing I would recommend is that someone has built a database of topological spaces that includes most of these, so if you can't afford/your library doesn't have this book try this website:https://topology.jdabbs.com/spaces
The action is first rate with things that may have seem far fetched just a couple of years ago but now seem really possible.
One can really tell that Lynn Arthur Steen knew what was being written, elements were explained accurately but not overly, and scenes were described with much detail.
Topology is abstract enough that if you are learning the subject for the first time, and you are not constantly challenging yourself to come up with concrete applications and counterexamples, you will probably learn very little. If you find the requirements of a particular theorem to be a bit over-the-top and find yourself a few brain cells short of coming up with a proper counterexample to illuminate why the theorem is stated in that way, this book will be extremely useful. Even if you can alwa...
Every student of topology should have this. Steen and Seebach provide instances to illustrate every distinction commonly made in topology (e.g. regular but not normal, T1 but not Hausdorff). In the latter part of the book the authors offer a thorough discussion of metrizability (under what conditions can a topological space be given a metric that "agrees" with its topology?).
As the title states, this book provides counterexamples in topology (that you were probably too lazy to come up with). Some of the examples were very critical in understanding topology at the undergraduate level, but as one may suspect, most of them were just so esoteric to the point of absurdity.
This is a great side-piece to peruse during your topology studies. Read it alongside Munkres. It's just what it sounds like - a big list of examples. It can enrich your topology skills and deepen your understanding. Also, it's jam-packed with fascinating stuff.
I might have debated whether to give this 4 or 5 starsif it had been a +$50 math book, but at $10, "the choice(function) is clear ..."
The Dover "Counterexamples in..." line is generally awesome; no exception here.
Topology