Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Let R be the set of real numbers and let B be the collection of all intervals of the form [a, b), where a < b. Show that B is a base for a topology on R. (Recall that [a, b) = {x | a

Let R be the set of real numbers and let B be the collection of all intervals of the form [a, b), where a < b. Show that B is a base for a topology on R. (Recall that [a, b) = {x | a

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
The chapter is on Bases.
1. Let \(\mathbb{R}\) be the set of real numbers and let \(\mathcal{B}\) be the collection of all intervals of the form \([a, b)\), where \(a < b\). Show that \(\mathcal{B}\) is a base for a topology on \(\mathbb{R}\). (Recall that \([a, b) = \{x \mid a \leq x < b\}\).)
Transcribed Image Text:1. Let \(\mathbb{R}\) be the set of real numbers and let \(\mathcal{B}\) be the collection of all intervals of the form \([a, b)\), where \(a < b\). Show that \(\mathcal{B}\) is a base for a topology on \(\mathbb{R}\). (Recall that \([a, b) = \{x \mid a \leq x < b\}\).)
Expert Solution
Step 1

Consider the provided question,

Given that, R be the set of real numbers and B be the collection of all intervals of the form [a,b), where a < b.

Here, [a,b)=x|a≤x<b

We have to prove that B is base or basis for a topology on R.

(i) For any x∈R, x∈[x, x+1). So, R is union of all members of B.

(ii) Consider the interval [a,b) and [c,d), where a<b and c<d.

 

 

 

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Research Ethics
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,
SEE MORE TEXTBOOKS