d if -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
topology
![Define \( p: \mathbb{R} \to Y \) by
\[
p(x) =
\begin{cases}
a & \text{if } x > 2 \\
b & \text{if } x = 2 \\
c & \text{if } 0 \leq x < 2 \\
d & \text{if } -1 < x < 0 \\
e & \text{if } x \leq -1
\end{cases}
\]
(a) List the open sets in the quotient topology on \(\{a, b, c, d, e\}\).
(b) Now assume that \(\mathbb{R}\) has the lower limit topology. What are the open sets in the resulting quotient topology on \(\{a, b, c, d, e\}\)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36268169-052e-482b-acb5-c5dcae700f3f%2F37792f49-1ac5-4bf9-a354-b955dcf28794%2Fy7oolen_processed.png&w=3840&q=75)
Transcribed Image Text:Define \( p: \mathbb{R} \to Y \) by
\[
p(x) =
\begin{cases}
a & \text{if } x > 2 \\
b & \text{if } x = 2 \\
c & \text{if } 0 \leq x < 2 \\
d & \text{if } -1 < x < 0 \\
e & \text{if } x \leq -1
\end{cases}
\]
(a) List the open sets in the quotient topology on \(\{a, b, c, d, e\}\).
(b) Now assume that \(\mathbb{R}\) has the lower limit topology. What are the open sets in the resulting quotient topology on \(\{a, b, c, d, e\}\)?
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