1. On the real line R with the usual metric (a) the set N of natural numbers is a closed set. (b) every closed interval is a closed set. (c) the set Q of rational numbers is not a closed set. 2. On the Euclidean plane R² with the usual metric

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

closed set Examples

1. On the real line R with the usual metric
(a) the set N of natural numbers is a closed set.
(b) every closed interval is a closed set.
(c) the set Q of rational numbers is not a closed set.
2. On the Euclidean plane R² with the usual metric
(a) the unit square U = {(x,y)|0 <x< 1, 0 < y < 1} is a closed
set.
(b) the set A = {(1+, 1 – )|n E N} is not a closed set.
(c) the set B = {(1, r)| r E Q} is not a closed set.
Transcribed Image Text:1. On the real line R with the usual metric (a) the set N of natural numbers is a closed set. (b) every closed interval is a closed set. (c) the set Q of rational numbers is not a closed set. 2. On the Euclidean plane R² with the usual metric (a) the unit square U = {(x,y)|0 <x< 1, 0 < y < 1} is a closed set. (b) the set A = {(1+, 1 – )|n E N} is not a closed set. (c) the set B = {(1, r)| r E Q} is not a closed set.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Relations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,