Ir X = {a,b, c, d, e, S} and T is the discrete topology on X, which of the following statements are true? (a) X € T; (e) Ø € X; (b) {X} € T; (c) {Ø} € T; (d) Ø € T; (f) {0} € X; U) {a} € X; (m) XCT; (n) {a} C T; (Hint. Precisely six of the above are true.) (9) {a} € T; (k) {0} X; (0) {X}ST; (h) a € T; (1) ØS X; (1) a e X; (p) a CT.
Ir X = {a,b, c, d, e, S} and T is the discrete topology on X, which of the following statements are true? (a) X € T; (e) Ø € X; (b) {X} € T; (c) {Ø} € T; (d) Ø € T; (f) {0} € X; U) {a} € X; (m) XCT; (n) {a} C T; (Hint. Precisely six of the above are true.) (9) {a} € T; (k) {0} X; (0) {X}ST; (h) a € T; (1) ØS X; (1) a e X; (p) a CT.
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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topolgy with justification to each one
![3. If X = {a,b, c, d, e, f} and T is the discrete topology on X, which of the following
statements are true?
(a) X € T;
(e) Ø e X;
(1) Ø C X;
(c) {Ø} € T;
(9) {a} € T;
(b) {X} € T;
(d) Ø € T;
(f) {Ø} € X;
(h) a € T;
1) {a} € X;
(k) {Ø} C X;
(0) {X} C T;
(Hint. Precisely six of the above are true.]
(1) a € X;
(m) X C T;
(n) {a} C T;
(p) a C T.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feeba0fbf-9265-4249-be46-5c587bce6ace%2Fa166c5ae-5ba1-4f88-ab42-027da5139374%2Fk9vky65_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. If X = {a,b, c, d, e, f} and T is the discrete topology on X, which of the following
statements are true?
(a) X € T;
(e) Ø e X;
(1) Ø C X;
(c) {Ø} € T;
(9) {a} € T;
(b) {X} € T;
(d) Ø € T;
(f) {Ø} € X;
(h) a € T;
1) {a} € X;
(k) {Ø} C X;
(0) {X} C T;
(Hint. Precisely six of the above are true.]
(1) a € X;
(m) X C T;
(n) {a} C T;
(p) a C T.
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