d T = {0, {a}, {a, b}, {c,d}, {a, c, d}, {a,b, c, d}, X}. (1) Is this space To? Why or why not? (2) Is this space T₁? Why or why not? (3) What is cl{a}?
d T = {0, {a}, {a, b}, {c,d}, {a, c, d}, {a,b, c, d}, X}. (1) Is this space To? Why or why not? (2) Is this space T₁? Why or why not? (3) What is cl{a}?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Exercise 2.** Consider the finite topological space \((X, \tau)\) where \(X = \{a, b, c, d, e\}\) and
\[
\tau = \{\emptyset, \{a\}, \{a, b\}, \{c, d\}, \{a, c, d\}, \{a, b, c, d\}, X\}.
\]
1. Is this space \(T_0\)? Why or why not?
2. Is this space \(T_1\)? Why or why not?
3. What is \(\text{cl}\{a\}\)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c557725-037f-4839-bada-f183764fca9b%2F4288d60b-f002-4919-bb27-5545e1ed3959%2Fa3k1c3e_processed.png&w=3840&q=75)
Transcribed Image Text:**Exercise 2.** Consider the finite topological space \((X, \tau)\) where \(X = \{a, b, c, d, e\}\) and
\[
\tau = \{\emptyset, \{a\}, \{a, b\}, \{c, d\}, \{a, c, d\}, \{a, b, c, d\}, X\}.
\]
1. Is this space \(T_0\)? Why or why not?
2. Is this space \(T_1\)? Why or why not?
3. What is \(\text{cl}\{a\}\)?
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