3. Ir X = {a,b, c, d,e, f} and T is the discrete topology on X, which of the following statements are true? (b) {X} € T; (f) {Ø} € X; U) {a} € X; (c) {O} € T; (a) X € T; (e) Ø E X; (1) Ø C X; (9) {a} € T; (k) {Ø} C X; (d) Ø € T; (h) a E T; (1) a € X; (n) {a} CT; (Hint. Precisely six of the above are true.) (0) {X} CT; (m) X C T; (p) a C T.

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ISBN:9780470458365
Author:Erwin Kreyszig
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topology with justifaction for 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.
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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