An Introduction to Topology and Homotopy by Allan J. Sieradski

By Allan J. Sieradski

The therapy of the topic of this article isn't really encyclopedic, nor used to be it designed to be compatible as a reference handbook for specialists. really, it introduces the subjects slowly of their ancient demeanour, in order that scholars aren't beaten through the final word achievements of a number of generations of mathematicians. cautious readers will see how topologists have steadily subtle and prolonged the paintings in their predecessors and the way such a lot strong rules achieve past what their originators expected. To inspire the improvement of topological instinct, the textual content is abundantly illustrated. Examples, too a variety of to be thoroughly coated in semesters of lectures, make this article compatible for self sufficient learn and make allowance teachers the liberty to pick what they're going to emphasize. the 1st 8 chapters are compatible for a one-semester path normally topology. the whole textual content is appropriate for a year-long undergraduate or graduate point curse, and gives a powerful starting place for a next algebraic topology direction dedicated to the better homotopy teams, homology, and cohomology.

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Thank you anon for the djvu add, I simply switched over and did ocr with tesseract. I didn't like Munkres kind (too verbose imo) this one is far better.

-- Reviews

when i used to be a pupil, this and Munkres have been the topology books opposed to which each different booklet used to be measured.

And whereas Munkres was once of a extra introductory style, this was once the true deal.


There are just a couple of vintage encyclopaedic texts on undergraduate topology, and Dugundji's is considered one of them. And between such books, this can be my favorite as the others are too outdated or too voluminous. Dugundji's e-book is brief, sleek, and impeccable. It covers each subject an undergraduate may still recognize or even extra. it really is nonetheless worthy for me after years of use. It exposes all very important options of set topology and provides a quick yet centred creation to algebraic topology.
You won't remorse to learn it.


One of the easiest Topology books i've got learn. although the e-book has no figures (as one might count on from a topology book), nearly each element is roofed and there usually are not imprecise elements within the proofs. for instance, the publication via Willard can be sturdy, yet in a few elements there are extra complicated information left for the reader. I took a easy topology graduate point path at the first 1/2 2007, which consisted on fixing the issues during this e-book. We have been capable of finding a few difficulties that requested to turn out anything fake, yet they have been 3 or 4 between all of the difficulties from sections III to VIII. besides, this e-book is a vintage that you can personal should you plan to paintings in topology or a minimum of learn it whereas learning the topic. It's only a disgrace that the e-book is out of print.

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More generally, this argument shows that any eventually periodic continued fraction whose periodic part is 1ր1 + 1ր2 + 1ր3 has as its √ value some number in the field Q( 37) . However, not all irrational numbers in this field have eventually periodic continued fractions with periodic part 1ր1 + 1ր2 + 1ր3 . √ For example, the continued fraction for 37 itself is 6 + 1ր12 , with a different periodic part. ) One Half of Lagrange’s Theorem The procedure we have used in these examples works in general for any irrational number z whose continued fraction is eventually periodic.

This is the number we use in the 2+1 next step. √ √ √ (2) 2 + 1 = 2 + ( 2 − 1) since 2 + 1 is between 2 and 3 . Notice that something unexpected has happened: The remainder r2 = √ 2−1 is exactly the same as the previous remainder r1 . There is then no need to do the calculation √ 1 since we know it will have to be 2 + 1 . This means that the next step of r12 = √2−1 (3) will be exactly the same as step (2), and the same will be true for all subsequent steps. Hence we get the continued fraction 1ր 1ր 2 = 1 +1ր 2 + 2 + 2 + ··· We can check this calculation by finding the value of the continued fraction in the same way that we did earlier for ր1 + 1ր1 + 1ր1 + · · · .

The next figure shows the simple example of the continued fraction for 3/8 . We can see here that the five triangles of the strip correspond to the four curvilinear triangles lying directly above 3/8 in the Farey diagram, plus the fifth ‘triangle’ extending upward to infinity, bounded on the left and right by the vertical lines above 0/1 and 1/1 , and bounded below by the semicircle from 0/1 to 1/1 . 1 − 0 1 − 0 1 − 0 1 3 2 3 4 1 1 2 −15 − 2 − 3 − 5 − 3 − 4 − 5 − 4 − 5 3 − 8 0 − 1 1 − 1 1 − 1 1 − 2 0 − 1 2 − 5 3 − 8 1 − 3 This example is typical of the general case, where the zigzag path for a continued fraction p q = a0 + 1րa1 + 1րa2 + · · · + 1րan becomes a ‘pinball path’ in the Farey diagam, starting down the vertical line from 1/0 to a0 /1 , then turning left across a1 triangles, then right across a2 triangles, then left across a3 triangles, continuing to alternate left and right turns until reaching the final vertex p/q .

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