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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
Great Read!!! Great story!!!
Format: Kindle
The series is long, but Ms. Wolfhart does a fantastic job of weaving this tale while bringing so much to the characters. Surprises and plot twists along the way to keep you intrigued. There is some graphic sex, but is no way the focal point. Grammar was excellent (a rare find with a lot of self publishers) with only a few noted errors. I rarely give 4 stars, let alone 5.
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Reviewed in the United States on April 30, 2021
★★★★★ 3
Sadly, DNF
Format: Kindle
I read this thru KU. I LOVED the synopsis. And then I began reading... and it was a DNF at 68% after picking it up and putting it down several times because I really loved the main female character.
*****SPOILERS*****
Pros:
The world is unique, intriguing and fun. The primary female character is bad-a** but not a b*tech or a mary sue. The primary female has depth. I really want to know what happens to her even tho it's been weeks and I don't remember her name. The villains to the point I read are pretty good -- an ever present threat of mysterious and possibly many culprits.
Cons:
Way, way too many points of view. I stopped counting at 7. It's the prime reason why I don't care about most of the characters or remember their names even when I like them. There's just too many points of view so almost none of the characters have enough book space for the author to properly develop them. This literally killed the book for me. Actually it killed my desire to read. For weeks.
The main male is more villain than hero. He agreed to marry the main female then locks her up & eschews her for her sister, all while bad mouthing her as unfit to rule when he never spent any time with her getting to know her. He is actually unfit to rule as he is blind to the woes of his own kingdom and starts off a peace mission to secure a ceasefire through marriage by murdering an inn full of people in her country for no real reason. Plus, he constantly makes promises he does not keep. And it's gross of him to pine for the sister behind the main female's back.
*****
As much as I really wanted to see what happened to the main female character, it wasn't enough for me to keep trying to slog thru this book. There was a lot of potential here that just fell short.
Hence, 3 stars.
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Reviewed in the United States on June 19, 2021
★★★★★ 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!
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on March 4, 2020
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