Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad

Hardcover (Print)
Buy New
Buy New from BN.com
$165.00
Eligible for FREE SHIPPING details
Usually ships within 24 hours details
Used and New from Other Sellers
Used and New from Other Sellers
from $85.00
Usually ships in 1-2 business days
(Save 48%)
Other sellers (Hardcover)
  • All (5) from $85.00   
  • New (4) from $85.00   
  • Used (1) from $238.89   

More About This Textbook

Overview

In topology the three basic concepts of metrics, topologies and uniformities have been treated so far as separate entities by means of different methods and terminology. This is the first book to treat all three as a special case of the concept of approach spaces. This theory provides an answer to natural questions in the interplay between topological and metric spaces by introducing a uniquely well suited supercategory of TOP and MET. The theory makes it possible to equip initial structures of metricizable topological spaces with a canonical structure, preserving the numerical information of the metrics. It provides a solid basis for approximation theory, turning ad hoc notions into canonical concepts, and it unifies topological and metric notions. The book explains the richness of approach structures in great detail; it provides a comprehensive explanation of the categorical set-up, develops the basic theory and provides many examples, displaying links with various areas of mathematics such as approximation theory, probability theory, analysis and hyperspace theory.

Read More Show Less

Product Details

  • ISBN-13: 9780198500308
  • Publisher: Oxford University Press, USA
  • Publication date: 8/28/1997
  • Series: Oxford Mathematical Monographs Series
  • Pages: 262
  • Product dimensions: 6.30 (w) x 9.20 (h) x 0.80 (d)

Table of Contents

Introduction 1
1 Approach Spaces 9
2 Topological Approach Spaces 72
3 Metric Approach Spaces 92
4 Uniform Approach Spaces 117
5 Canonical Examples 136
6 Approach Properties 167
7 Completion 190
8 Compactification 203
App. A.1 Basic Categorical Concepts 218
App. A.2 Topological Constructs 224
App. A.3 Reflective and Coreflective Subconstructs 228
App. B.1 Metric Spaces 231
App. B.2 Probabilistic Metric Spaces 234
App. B.3 Convergence Spaces 236
App. B.4 Quasi-Uniform and Uniform Spaces 238
App. B.5 Proximity Spaces 240
Bibliography 241
Index 249
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Review Guidelines
Add Recommendations
Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously
    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)