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Description
Elements of the Theory of Functions and Functional AnalysisOriginally published in two volumes, this advanced level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow. Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and
Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces -- a topic seldom discussed in textbooks.
Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.
Binding Type: Paperback
Publisher: Dover Publications
Published: 02/16/1999
ISBN: 9780486406831
Pages: 288
Weight: 0.64lbs
Size: 8.47h x 5.40w x 0.52d
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4.2 ★★★★★
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Product Reviews
★★★★★ 4
not bad
Format: Kindle
I loved the plot of this book. The characters just didn’t have a lot of depth. The connections and “love” just weren’t communicated very well in the writing. The author didn’t write the sweet psycho trope very well at all either. Lachlan was just a mess of a character.
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Reviewed in the United States on November 17, 2023
★★★★★ 5
A Beta Worth Rooting For
Format: Kindle
In Spare, Violet Fox flips the omegaverse on its head, giving us a Beta heroine determined to make her mark. Joining the Beta Trials to support her sick father, she's thrown into a pack that doesn't want her, especially the possessive Alphas.
But here's the twist: their sweet Omega turns out to be her scent match. Cue the angst, forbidden tension, and a slow-burn romance that will make your heart ache in the best way.
Violet Fox delivers an emotional, refreshing take on the genre, proving Betas aren't "spares." They're stars.
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Reviewed in the United States on January 10, 2025
★★★★★ 5
Beta, Alpha, Omega oh my!
Format: Kindle
Omegas are precious and given to Alphas & their packs... but the Betas want in too. To this end, the Beta government is rolling out its trial of assigning a Beta to each Alpha-Omega pack. But forcing a Beta into a pack where they are not wanted will not end well... Of course, no one expected the Omega to fall for the assigned Beta. Great read and cliffhanger
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Reviewed in the United States on February 15, 2025
★★★★★ 3
A familiar story, just with…..less.
Format: Kindle
So, as other reviewers make clear, this is very similar to Pack Darling and The Beta. It’s much closer aligned with The Beta, in plot and maybe more like Pack Darling with characters.
That being said, I don’t hate this…..but it wasn’t great either. It’s both books mentioned but just….less. Less angst, less emotion, less feeling. The plot feels very half fleshed out, and the “bad guy” feels underwhelming. I didn’t really feel any real emotions from and of the male leads, except maybe Oliver. The others fell sorta flat for me. And Mika makes herself out to be this big bad ass straight outta training and then we never see it from here again with the one fitting room incident as the exception.
SPOILER:
The whole, “Oh, I’m actually probably an Omega, but I don’t wanna be but I do actually wanna be but no one can ever know my secret that I do nothing to hide “ thing fell so flat. She never commutes to believing she was secretly an omega, but also mentions her “secret” a lot. It just felt so manufactured.
I’m intrigued enough to read part 2 and see how the author closes everything out, but this is not one I’ll recommend or ever come back to.
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Reviewed in the United States on February 13, 2024
★★★★★ 5
Wow.
Format: Kindle
Okay I’m usually not one for stand-alone’s I’m an avid series reader but my goodness am I so happy I read this! This story was brilliant & so absolutely mesmerizing. I loved reading about each character and their struggles as well as what helped them to move forward. The ending definitely brought tears to my eyes so hard. I truly wasn’t expecting some of what happened in this story. There is about to be a spoiler I am going to reveal so please stop reading if you don’t want the spoiler !!!! ⚠️ ⛔️ ‼️
I loved that the author didn’t do what most authors do with irredeemable male characters. I truly was hoping that Nate Jr. would be apart of the pack after the way he treated Astrea bc he truly didn’t deserve it. Though I must say you did a wonderful job or redeeming him as a person. I cried my eyes out when he walked into the story. I was truly terrified he was going to be a bad guy to the end. However you truly did him such a justice by having him realize his faults & having him redeem himself in the most wonderful way. I’m so sad that he didn’t get to hear how much his brother loved him & forgave him before dying. But again you wrote that ending so beautifully & I just can’t express how much I loved this story & how you took a different route than most authors I have read have. You are a remarkable author Cinder Blaze & I thank you generously for creating such a masterpiece.
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Reviewed in the United States on April 28, 2025