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Description
Introduction to Topology: Second EditionOne of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics. While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point set topology material is treated in the first two chapters;
One of the most important milestones in mathematics in the twentieth century was the development of topology as an independent field of study and the subsequent systematic application of topological ideas to other fields of mathematics.While there are many other works on introductory topology, this volume employs a methodology somewhat different from other texts. Metric space and point-set topology material is treated in the first two chapters; algebraic topological material in the remaining two. The authors lead readers through a number of nontrivial applications of metric space topology to analysis, clearly establishing the relevance of topology to analysis. Second, the treatment of topics from elementary algebraic topology concentrates on results with concrete geometric meaning and presents relatively little algebraic formalism; at the same time, this treatment provides proof of some highly nontrivial results. By presenting homotopy theory without considering homology theory, important applications become immediately evident without the necessity of a large formal program.
Prerequisites are familiarity with real numbers and some basic set theory. Carefully chosen exercises are integrated into the text (the authors have provided solutions to selected exercises for the Dover edition), while a list of notations and bibliographical references appear at the end of the book.
Binding Type: Paperback
Publisher: Dover Publications
Published: 02/16/1999
ISBN: 9780486406800
Pages: 256
Weight: 0.69lbs
Size: 9.20h x 6.15w x 0.48d
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Product Reviews
★★★★★ 5
Fae Courts with High Intrigue
Format: Kindle
This book is one that just builds and builds and then surprises you to no end. You may think you know the villains and then you are jolted in another direction. Princess Reyna is a real gem, strong of character, a fierce fighter, and loyal to her family and kingdom. Just when you think she and Lorcan, well you know, the plot is flipped. Can't wait to see where this goes in book two.
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Reviewed in the United States on July 7, 2023
★★★★★ 4
Slow, sorry but good
Format: Kindle
This was a slow moving book. Lots of character pov chapters, lots of superfluous descriptions and endless courtly appearances stalled this book to start. Once you get into the heart of the story, it takes off. Before you know it the book is done. My favorite character is Reyna. She is so strong. She is true to herself. She gets into a lot of trouble with her headstrong ways but it's entertaining. I have high hopes for Lorcan. He is honorable to a fault. Thane had turned out to be better than I thought but i still don't like him. Eislin is useless. Great plot twists at the end. I'm looking forward too book 2.
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Reviewed in the United States on June 6, 2020
★★★★★ 5
Very detailed! Beautiful world building! Strong Heroine!
Format: Kindle
Starts off a little slow and confusing with different POV’s, but starts to all come together towards the middle to make an elaborate plot line and makes it all worth it. Beautiful world building and attention to detail as well as great writing. The cliffhanger was gut wrenching! Can’t wait for the next book!
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Reviewed in the United States on March 4, 2020
★★★★★ 4
Interesting
Format: Kindle
This was a very captivating book once you got into it thoroughly. But the third person perspective was a bit hard to get used to. But as you got into it and followed the different characters, it was interesting and filled with intrigue, conflict and forbidden love.
I can’t wait to read the next one and to complete the series.
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Reviewed in the United States on November 12, 2022
★★★★★ 5
OUTSTANDING
Format: Kindle
This was very, very good. The world is vast and characters are complex. There is a good plot with a whole lot going on. This is well written. Good twists and turns and some heart breaking moments. You will love these characters, they have heart and loyalty. I am hoping that there will be several more books. We've yet to see anything from the Sea Court but only a mention of them here and there. The Wood Court was given a quick couple of scenes, and only as far as some warriors, we've yet to enter their court and the Shadow Court, I'm not sure if they will be a force for good or bad, but they definitely will play a much bigger role moving forward. This is primarily the Ice and Air Courts. Told in multiple views, which I loved, it gives you a chance to see things from different eyes. There's alot of political maneuvering and deception. I loved it and will pick up the next book as it becomes available. If you like The Fae and the courts, you should love this. I think the author has mucn in store for us.
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Reviewed in the United States on March 8, 2020
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