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X be given by J1(3 2. Let X be the set of real numbers, let U be the usual topology, and let D be the discrete topology. Suppose f: X-X is given by f(z)=z³. Which of the following are continuous? Explain. (a) f: (X,U)-(X.D). (b) f: (X,D)-(X,U). topological space into another.

X be given by J1(3 2. Let X be the set of real numbers, let U be the usual topology, and let D be the discrete topology. Suppose f: X-X is given by f(z)=z³. Which of the following are continuous? Explain. (a) f: (X,U)-(X.D). (b) f: (X,D)-(X,U). topological space into another.

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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1. Let X be the space of fea X be given by f(x)=³. Show that f is continuous. 2. Let X be the set of real numbers, let U be the usual topology, and let D be the discrete topology. Suppose f: X-X is given by f(x)=z³. Which of the following are continuous? Explain. (a) f: (X,U)-(X.D). (b) f: (X.D) (X,U). tonological space into another.
Transcribed Image Text:1. Let X be the space of fea X be given by f(x)=³. Show that f is continuous. 2. Let X be the set of real numbers, let U be the usual topology, and let D be the discrete topology. Suppose f: X-X is given by f(x)=z³. Which of the following are continuous? Explain. (a) f: (X,U)-(X.D). (b) f: (X.D) (X,U). tonological space into another.
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