Assuming a basic knowledge of real analysis and linear algebra, the student is given some familiarity with the axiomatic method in analysis and is shown the power of this method in exploiting the fundamental analysis structures underlying a variety of applications. Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition brings an interesting link with linear algebra; finite dimensional spaces are discussed earlier. It is intended that metric spaces be studied in some detail before general topology is begun. This follows the teaching principle of proceeding from the concrete to the more abstract. Graded exercises are provided at the end of each section and in each set the earlier exercises are designed to assist in the detection of the abstract structural properties in concrete examples while the latter are more conceptually sophisticated.
FREE Two-Day Shipping for students on millions of items. Learn more |
| |||||||||||||||
Book Description
Editorial Reviews
Book Description
Although the text is titled metric spaces, normed linear spaces are introduced immediately because this added structure is present in many examples and its recognition develops an interesting link with linear algebra.
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
First Sentence:
After some experience with real and complex analysis it becomes apparent that the development of the theory depends to a great extent simply on the notion of distance between the numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
following real functions, dimensional normed linear space, normed linear subspace, linear space operations, cover compactness, discrete metric space, same scalar field, normed linear spaces, characterisation theorem, nonmed linear space, single point set, metric subspace, pointwise convergent, pointwise definition, ternary representation, total boundedness, usual norm, compact metric space, isometric isomorphism, finite subcover, global continuity, local compactness, cluster point, sequential compactness, norm property Key Phrases - Capitalized Phrases (CAPs): (learn more)
Weierstrass Approximation Theorem, Stone-Weierstrass Theorem, Peano's Theorem, Heine's Theorem, Picard's Theorem, Riesz Theorem, Dini's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
After some experience with real and complex analysis it becomes apparent that the development of the theory depends to a great extent simply on the notion of distance between the numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
following real functions, dimensional normed linear space, normed linear subspace, linear space operations, cover compactness, discrete metric space, same scalar field, normed linear spaces, characterisation theorem, nonmed linear space, single point set, metric subspace, pointwise convergent, pointwise definition, ternary representation, total boundedness, usual norm, compact metric space, isometric isomorphism, finite subcover, global continuity, local compactness, cluster point, sequential compactness, norm property Key Phrases - Capitalized Phrases (CAPs): (learn more)
Weierstrass Approximation Theorem, Stone-Weierstrass Theorem, Peano's Theorem, Heine's Theorem, Picard's Theorem, Riesz Theorem, Dini's Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
books:
17
books
cite this book:
See all 17 books citing this book
- Introduction to Linear and Convex Programming (Australian Mathematical Society Lecture Series) by Neil Cameron in Front Matter
- Foundations of modern analysis (Pure and applied mathematics; a series of monographs and textbooks) by Jean Alexandre Dieudonne in Front Matter
- Manifolds and Mechanics (Australian Mathematical Society Lecture Series) by Arthur Jones in Front Matter
- New South (Yale chronicles of America series) by Holland Thompson in Front Matter
- Mathematical Methods and Models for Economists by Angel de la Fuente on page 114, and page 154
- Chaos: A Mathematical Introduction (Australian Mathematical Society Lecture Series) by John Banks in Front Matter
- Modelling with Differential and Difference Equations (Australian Mathematical Society Lecture Series) by Glenn Fulford in Front Matter
- The Petersen Graph (Australian Mathematical Society Lecture Series) by D. A. Holton in Front Matter
- Geometric Analysis and Lie Theory in Mathematics and Physics (Australian Mathematical Society Lecture Series) by Alan L. Carey in Front Matter
See all 17 books citing this book
Books on Related Topics
(learn more)
|
What Other Items Do Customers Buy After Viewing This Item?
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Sell a Digital Version of This Book in the Kindle Store
If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.
Learn more
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
Listmania!
|
|
So You'd Like to...
|
|
