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4. (0} is open in Y. a. True b. False

4. (0} is open in Y. a. True b. False

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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Topology Answer of number 4 with justification
Let N be endowed with the discrete topology and Y = {0}U nEN- (0,1 %3D 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) = Vn > 1. 1. f 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. f is continuous. a. True b. False 6. f is a homeomorphism. a. True h. False a
Transcribed Image Text:Let N be endowed with the discrete topology and Y = {0}U nEN- (0,1 %3D 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) = Vn > 1. 1. f 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. f is continuous. a. True b. False 6. f is a homeomorphism. a. True h. False a
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