Let X = {a,b, c, d},T = {0, X, {d}, {a,b}, {a,b, d}}and Y = {m,n, p,q}, F = {o,Y, {p},{m,n},{m,n,p}}Given the mapping f: (X,r) -→ (Y, F) byf(a) = m, f(b) = n, f(d) = p, f(c) = q.Thena. f is a continuous but not open mapping.b. f is an open but not continuous mapping.c. f is neither continuous nor open mapping.d. f is a continuous and open mapping. Q. One of the following is wrong:a. Connectedness is a topological property;b. Pathwiseconnectednes is a topological property.c. Fixed point property is a topological property.d. Preserving area is a topological property.

according to our guidelines we can answer only three subparts, or first question and rest can be…

Let X = {a,b, c, d},T= {ø, X, {d}, {a,b}, {a,b, d}} and Y = {m,n,p,q},F = {0,Y, {p},{m,n}, {m, n,p}} Given the mapping f: (X,) → (Y. F) by f(a) = m, f (b) = n, f(d) = p, f(c) = q.Then a. f is a continuous but not open mapping. b. f is an open but not continuous mapping. c. f is neither continuous nor open mapping. d. f is a continuous and open mapping.

Let X = {a,b, c, d},T= {ø, X, {d}, {a,b}, {a,b, d}} and Y = {m,n,p,q},F = {0,Y, {p},{m,n}, {m, n,p}} Given the mapping f: (X,) → (Y. F) by f(a) = m, f (b) = n, f(d) = p, f(c) = q.Then a. f is a continuous but not open mapping. b. f is an open but not continuous mapping. c. f is neither continuous nor open mapping. d. f is a continuous and open mapping.

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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