Let N be endowed with the discrete topology and Y = (0} U<,nEN-(0.1)> be a subspace ofR. The topology on Y is the induced topology by the Euclidean topology on R. We define the functionS:N-(0}- Y by f(1) = 0 and f(n)=Vn > 1.1. is a one to one function.a Trueb. False2. f is onto.a Trueb. False3. f is continuous.a. Trueb. False4. (0} is open in Y.a. Trueb. False5. is continuous.a. Trueb False6. f is a homeomorphism.a. Trueb. False

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Let N be endowed with the discrete topology and Y = (0} u, nEN- (0, 1}> be a subspace of R. The topology on Y is the induced topology by the Euclidean topology on R. We define the function f:N-(0} Y by f(1) 0 and f(n) = , %3D Vn > 1. 1. is a one to one function. a True b. False 2. f is onto. a True b. False 3. f is continuous. a. True b. False 4. (0} is open in Y. a. True b. False 5. is continuous. a. True b. False 6. f is a homeomorphism. a. True b. False

Let N be endowed with the discrete topology and Y = (0} u, nEN- (0, 1}> be a subspace of R. The topology on Y is the induced topology by the Euclidean topology on R. We define the function f:N-(0} Y by f(1) 0 and f(n) = , %3D Vn > 1. 1. is a one to one function. a True b. False 2. f is onto. a True b. False 3. f is continuous. a. True b. False 4. (0} is open in Y. a. True b. False 5. is continuous. a. True b. False 6. f is a homeomorphism. a. True b. False

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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