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Description
Elementary Point-Set Topology: A Transition to Advanced MathematicsIn addition to serving as an introduction to the basics of point set topology, this text bridges the gap between the elementary calculus sequence and higher level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and
In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses.Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations.
"This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." -- Mathematical Association of America
Binding Type: Paperback
Publisher: Dover Publications
Published: 05/18/2016
ISBN: 9780486803494
Pages: 256
Weight: 0.70lbs
Size: 8.90h x 6.00w x 0.50d
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4.9 ★★★★★
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Product Reviews
★★★★★ 3
Comes with pump
Color: Colorful, Size: Large
My dogs enjoyed it but it’s not large dog proof. I have a husky and German Shepard…..the ball lasted a day before it was torn up. But this would be perfect for smaller or medium sized dogs.
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Reviewed in the United States on March 27, 2026
★★★★★ 5
Great toy
Color: Colorful, Size: Medium
Best toy ever for my Aussie!
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Reviewed in the United States on May 31, 2026
★★★★★ 5
Our German Sheppard loves these
Size: Medium
These cost a bit more than tennis balls, but they are so much nicer and longer lasting. For starters, they stay cleaner than tennis balls because they’re smooth rubber. Dirt won’t build up on them and if anything does stick, like grass or soil, it falls off once the dog slobber dries. They’re also thick, so they don’t fall apart or blow out like a normal tennis ball does in our dog’s jaws after 30 seconds. Our GS chomps on these like crazy and the only damage they’ve suffered is a crack that developed from the edge of the hole, but the crack is growing very slowly and none of these balls have totally failed yet. The balls do whistle when thrown ant high speed and that may help a dog track and locate it, but I’m not sure. Our neighbors hear the whistling too so it’s far from silent. Lastly the orange ball is easy to locate out in our yard, but the dark blue practically disappears.
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Reviewed in the United States on April 6, 2025
★★★★★ 5
Great for smaller dogs
Size: Small
These two balls are perfect for the smaller mouthed dog that loves to play fetch.
These balls are not only super durable (lots of teeth biting), but float in the baby pool we use for our miniature dachshunds.
The value here is much better than you’d find anywhere else. The noise, if bitten hard enough, was “low” at best. Easy to spot/find if overthrown. Will definitely buy again once these are in bad repair; so far, so good-love these for my fur babies!
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Reviewed in the United States on October 8, 2024
★★★★★ 5
My dogs favorite balls
Size: Medium
These are great for my dog who always has to have a ball in her mouth. Not too hard so I don't have to worry about her teeth. They last for ever. They do lose their shape a little over time (like I said, she always has a ball in her mouth) they become a little oval in shape. They still bounce, she still chases it and she still chews on it so I don't think she notices or cares. I've gotten her a bag full of these over time and I have only seen one that she chewed a chunk out.
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Reviewed in the United States on September 28, 2023
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