Topology Answer number 3 with justification Let N be endowed with the discrete topology and Y= {0}U, nEN-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 S(n)Vn > 1.1. f 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. f- is continuous.a. Trueb. False6. f is a homeomorphism.a. Trueb. False

Name: Topology Answer number 3 with justification Let N be endowed with the
Uploaded: 2024-03-20T06:38:58.000Z
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Description: Topology Answer number 3 with justification Let N be endowed with the discrete topology and Y= {0}U, nEN-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 S(n)Vn

We will show that f is continuous map

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Let N be endowed with the discrete topology and Y = (0} UnEN- 1-(0,1} be a s %3D R. The topology on Y is the induced topology by the Euclidean topology on R. We define th S:N-(0}Y by f(1) =0 and S(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