D 31%RingtoneYou22 April, 22:2510. Let (X, Tx) and (Y, Ty) be two topological spaces, such thatX = {a, b,c, d}, Tx = {ó, X, {a}, {a, b}, {a, b, c}}Y = {1,2, 3, 4}, Ty = {ó,Y, {2}, {2,3, 4}}Consider the functions f: X + Y and g: X +Y defined byf(a) = f(b) = 2, f(c) = 4, ƒ(d) = 3g(a) = g(b) = g(d) = 2, g(c) = 3Then(a) f and g are both continuous(b) f and g are both discontinuous(c) f is discontinuous and g is continuous(d) f is continuous and g is discontinuous

Answered: Image /qna-images/answer/c393a279-d54b-4513-b16c-c39ea7e77c05.jpg

10. Let (X, Tx) and (Y, Tr) be two topological spaces, such that X = {a, b,c, d}, Tx = {ó, X, {a}, {a, b}, {a, b,c}} Y = {1,2,3, 4), Ty = {6,Y, (2), (2,3, 4}} Consider the functions f: XY and g: X+Y defined by f(a) = f(b) = 2, f(e) = 4, f(d) = 3 g(a) = 9(b) = 9(d) = 2, g(c) =3 Then (a) f and g are both contimuous (b) f and g are both discontinuous (c) f is discontinuous and g is continuous (d) f is contimuous and g is discontinuous

10. Let (X, Tx) and (Y, Tr) be two topological spaces, such that X = {a, b,c, d}, Tx = {ó, X, {a}, {a, b}, {a, b,c}} Y = {1,2,3, 4), Ty = {6,Y, (2), (2,3, 4}} Consider the functions f: XY and g: X+Y defined by f(a) = f(b) = 2, f(e) = 4, f(d) = 3 g(a) = 9(b) = 9(d) = 2, g(c) =3 Then (a) f and g are both contimuous (b) f and g are both discontinuous (c) f is discontinuous and g is continuous (d) f is contimuous and g is discontinuous

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

(iii) If (X,r) is topological space, A,BCX. Prove that (a) b(A)=AA (b) If ACB, then d(A)
Let (X,T) and (Y,T1) be two topological spaces and let f be a continuous mapping of X into Y. * If (Y,T1) is a T1 space, then (X,T) is a T1 space None of the choices If f is onto and (Y,T1) is a Hausdorff space, then (X,T) is a Hausdorff space If f is one to one and (Y,T1) is a Hausdorff space, then (X,T) is a Hausdorff space
Let fít) = 1,2+1,1,1)||, What is the minimum value of this function of t ? Answer the same question for the functiong defined by g(t) = |(1,2 +1,7– )||.
Let (X, τ ) be a discrete space. Is (X, τ ) second countable? Explain why
Let (¥,r) and (¥ ,4) be two topological spaces. Prove that a function f :(X .r)——(¥ ,A) is continuous if and only if the inverse image under / of every A- closed set is a r- closed set.
Let X and Y be two topological sPaces. Let A and B be such that Ā=B. let f:X » Y be a Continuous function. Show that F(A)=f (B).
1. Let = (1, 2). a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) · √ = 0}. b. Draw the the points in set S in a Cartesian plane.
15. Let f: A → B and g: C → D. Define fx g = {(a, c), (b, d): (a, b) = f and (c,d) = g}. (a) Prove that f × g is a mapping from A × C to B x D. (b) For (a, c) = A x C, write (f× g)(a, c) in terms of f(a) and g(c).
Let (X, T) and (Y, T₁) be two topological spaces and let f be a continuous mapping of X into Y. None of the choices. If f is onto and (Y,T_1) is a Hausdorff space then (X,T) is Hausdorff. If f is one-to-one and (Y,T_1 ) is a Hausdorff space then (X,T) is Hausdorff. If (Y,T_1) is a T_1 space then (X,T) is a T_1 space. O
topology
Let f(x,y)=g(x)h(y) where g and h are continuous functions on all real numbers such that g(x)=h(x+1) and R={(x,y) | 1 ≤ x ≤ 2, 2 ≤ y ≤3}. Consider the following statements (image)a. Only statement 2. is true b. All statements are false c. All statements are true d. Only 1 and 2 are true e. Only statement 3. is true f. Only 2 and 3 are true g. Only 1 and 3 are true h. Only statement 1. is true
tX, Y be topological spaces and f: X Y be a continuous map. If X is completely normal then Y is also completely normal.