General topology books
Mali_42
of topology ?
Is there some problem book with solutions ?
Thanks
Spiros Bousbouras
> Which books should I look into for introductory and advanced level
> of topology ?
You'll get better answers if you specify how much mathematics you
already know but generally speaking I recommend:
General topology by Kelley
General topology by Engelking
I have also heard good things about Topology by James Munkres
> Is there some problem book with solutions ?
Fundamentals of General Topology: Problems and Exercises
by A.V. Arkhangelskii , V.I. Ponomarev
--
Who's your mama?
Stephen J. Herschkorn
You can't go wrong with Munkres. I also like Kelley, which includes
topics not in Munkres (and Kelley does not cover algebraic topology, as
Munkres does). However, Kelley is much earlier, so you might find the
pedagogical style in Munkres easier to follow.
For self-study, it doesn't hurt to have a few on your shelf. Some like
Hocking and Young (that's one book) and Willard (another), which are
both available in Dover. Personally, I haven't found them very useful.
Above all, go to a university library and peruse the section where there
are topology textbooks. See which one you like.
--
Stephen J. Herschkorn sjher...@netscape.net
Math Tutor on the Internet and in Central New Jersey
Spiros Bousbouras
wrote:
> Mali_42 wrote:
> >Which books should I look into for introductory and advanced level
> >of topology ?
> >Is there some problem book with solutions ?
>
As long as one doesn't constantly jump between different books. I
think the right approach when learning is to concentrate on one
which seems understandable and ideally also has a good reputation
and only look elsewhere when some proof in the chosen book seems
hopeless.
> Some like
> Hocking and Young (that's one book) and Willard (another), which are
> both available in Dover. Personally, I haven't found them very useful.
Not familiar with Hocking and Young but I agree about Willard whose
proofs I find unnecessarily complicated compared to Kelley's book.
One example is Urysohn's lemma , another is the proof that regular and
Lindelöf imply normal.
> Above all, go to a university library and peruse the section where there
> are topology textbooks. See which one you like.
If he is lucky enough to be living in a place where university
libraries have their doors open to the general public.
Stephen J. Herschkorn
On 17 June, 19:37, "Stephen J. Herschkorn" <sjhersc...@netscape.net> wrote:For self-study, it doesn't hurt to have a few on your shelf.As long as one doesn't constantly jump between different books. I think the right approach when learning is to concentrate on one which seems understandable and ideally also has a good reputation and only look elsewhere when some proof in the chosen book seems hopeless.
That said, I do find it easier to use one textbook as a main source and work through it. Also, books are not usually organized the same way. For example, Kelley introduces separability and connectedness much earlier, and compactness (and even continuity) much later, than Munkres.
A N Niel
> Is there some problem book with solutions ?
Schaum's Outline?
Spiros Bousbouras
wrote:
> Spiros Bousbouras wrote:
> >On 17 June, 19:37, "Stephen J. Herschkorn" <sjhersc...@netscape.net>
> >wrote:
>
> >>For self-study, it doesn't hurt to have a few on your shelf.
>
> >As long as one doesn't constantly jump between different books. I
> >think the right approach when learning is to concentrate on one
> >which seems understandable and ideally also has a good reputation
> >and only look elsewhere when some proof in the chosen book seems
> >hopeless.
>
> I disagree. When one takes a class, one often sees presentation of the
> material from two different perspectives, viz., those of the teacher and
> of the textbook's author. In self-study, one loses the first. Seeing
> several presentations helps give an impression of what is important (by
> their common appearances). And seeing two different presentations of
> the same topic often yields greater insight. One could learn much by
> parallel reading.
I think that for someone who's new to a topic and perhaps lacks
mathematical maturity the chance for greater confusion by
simultaneously reading different presentations is much greater than
the chance for greater insight. I'm influenced in this opinion by
having observed cranks who seem to have looked into many books
but have understood very little. When encountering such a case I
wonder whether they would have done much better if they had only
concentrated on one book and really took the effort to understand
it.
When I made the comment about jumping between different books I had
in mind someone who studies on their own. If someone attends a
class then they can ask the instructor questions which hopefully
will alleviate any confusion. Beyond that if there is significant
discrepancy between the content of the lectures and the content of
the textbook then I believe most students will just concentrate on
the lectures and pay little attention to the textbook because that
approach gives them the highest chance of passing the exam. So even
in such a context they will not really get exposed to 2 different
presentations.
Regarding finding out what's important, to some extent I agree. To
achieve this one can browse through a few books on the same topic
to see what's common. One ideally would do this anyway in order to
choose one to study. But I still feel that the actual studying is
best done from one book.
> That said, I do find it easier to use one textbook as a main source and
> work through it. Also, books are not usually organized the same way.
> For example, Kelley introduces separability and connectedness much
> earlier, and compactness (and even continuity) much later, than Munkres.
--
The Germans, we are given to understand, hate us with a bitter hatred,
and long to believe that we feel toward them as they feel toward us;
for unrequited hatred is as bitter as unrequited love.
Bertrand Russell
FredJeffries
> Which books should I look into for introductory and advanced level
> of topology ?
For an introduction I liked George Simmons "Introduction to Topology
and Modern Analysis" which I see is back in print:
http://www.amazon.com/Introduction-Topology-Modern-Analysis-Simmons/dp/1575242389
> Is there some problem book with solutions ?
There's a Schaum's Outline by Seymour Lipschutz
>
> Thanks
MoeBlee
> > Is there some problem book with solutions ?
>
> Schaum's Outline?
I really like Lipschutz's Schaum's book on topology. It's a good
supplement, and even wouldn't be terribly bad as a main textbook.
Meanwhile, its seems to me that Munkres is the most often recommended.
MoeBlee
Pete Klimek
news:4A393FD7...@netscape.net...
I disagree. When one takes a class, one often sees presentation of the
material from two different perspectives, viz., those of the teacher and of
the textbook's author. In self-study, one loses the first. Seeing several
presentations helps give an impression of what is important (by their common
appearances). And seeing two different presentations of the same topic
often yields greater insight. One could learn much by parallel reading.
That said, I do find it easier to use one textbook as a main source and work
through it. Also, books are not usually organized the same way. For
example, Kelley introduces separability and connectedness much earlier, and
compactness (and even continuity) much later, than Munkres.
Stephen J. Herschkorn sjher...@netscape.net
Math Tutor on the Internet and in Central New Jersey "
I agree with the idea that having one main textbook for self-study is the
way to go. I'm studying Munkres right now, but also own Kelley and Willard.
As Stephen noted, the three books introduce certain notions at different
places. For example, Munkres covers connectedness in chapter 3, while
Willard doesn't discuss this concept until chapter 8, making his examples
hard for me to follow. Actually, I use the other books for hints on Munkres'
exercises (one author's exercise is another's theorem).
Pete Klimek
Frederick Williams
>
> Which books should I look into for introductory
If you want something short--which can be a good idea when you're
starting out: big books can intimidate--try Bert Mendelson's
'Introduction to Topology'.
> and advanced level
> of topology ?
> Is there some problem book with solutions ?
>
> Thanks
--
... when we came back, late, from the hyacinth garden,
Your arms full, and your hair wet, I could not
Speak, and my eyes failed...
Narcoleptic Insomniac
I'll give another vote for Munkres' "Topology" text. Not
only does it cover both point-set and algebraic topology,
but it is one of the standards in many universities. As
for a solutions manual, I personally have never looked for
one... but I would imagine that several people have
attempted to create a solutions manual. (I haven't read
the entire thread; hopefully someone more familiar and
knowledgeable in this field has answered this.)
Good Luck,
Kyle Czarnecki
qsymmetry
>
[1] Fundamentals of General Topology: Problems and Exercises by A.V. Arkhangel'skii and V.I. Ponomarev
[2] Elementary Topology: Problem Textbook (Hardcover)
by O. Ya. Viro e.a.