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Q4. Let X = {m,n, pP. 9}, T = {6. X, {p}, {m, n}, {m,n.p}} and Y = {a, b, c, d}. F = {ó, X, {d}. {a, b}, {a, b, d}} Given the mapping f: (X,7) – (Y, F) by f(m) = a, f(n) = b, fp) = d, f(q) = c. Isfa bijection? Isfa continuous mapping? Is f an open mapping? Isfa homeomorphism ? What you can say about the topological spaces (X, 7) and (Y, F). ( Show the details of your answers).

Q4. Let X = {m,n, pP. 9}, T = {6. X, {p}, {m, n}, {m,n.p}} and Y = {a, b, c, d}. F = {ó, X, {d}. {a, b}, {a, b, d}} Given the mapping f: (X,7) – (Y, F) by f(m) = a, f(n) = b, fp) = d, f(q) = c. Isfa bijection? Isfa continuous mapping? Is f an open mapping? Isfa homeomorphism ? What you can say about the topological spaces (X, 7) and (Y, F). ( Show the details of your answers).

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
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Q4. Let X = {m, n, p, q}, T = {0, X, {p}, {m, n}, {m,n, p}} and Y = {a, b, c, d}, F = {6, X, {d}, {a, b}, {a, b, d}} Given the mapping f: (X,7) (Y, F) by f(m) = a, f(n) = b, f(p) = d, f(9) =. = e. Is fa bijection? Is fa continuous mapping? Is f an open mapping? Is fa homeomorphism ? What you can say about the topological spaces (X,T) and (Y, F). ( Show the details of your answers).
Transcribed Image Text:Q4. Let X = {m, n, p, q}, T = {0, X, {p}, {m, n}, {m,n, p}} and Y = {a, b, c, d}, F = {6, X, {d}, {a, b}, {a, b, d}} Given the mapping f: (X,7) (Y, F) by f(m) = a, f(n) = b, f(p) = d, f(9) =. = e. Is fa bijection? Is fa continuous mapping? Is f an open mapping? Is fa homeomorphism ? What you can say about the topological spaces (X,T) and (Y, F). ( Show the details of your answers).
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