3. Let T be the usual topology on IR. (i) Prove that the interval [-1, 1] is homeomorphic to the interval [2, 3], with the subspace topologies in (R, T). (ii) Is [2, 3] homeomorphic to R? State any results that you are using.

3. Let T be the usual topology on IR. (i) Prove that the interval [-1, 1] is homeomorphic to the interval [2, 3], with the subspace topologies in (R, T). (ii) Is [2, 3] homeomorphic to R? State any results that you are using.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

3. Let T be the usual topology on R.
(i) Prove that the interval [-1, 1] is homeomorphic to the interval [2, 3], with the
subspace topologies in (R, T).
(ii) Is [2, 3] homeomorphic to R? State any results that you are using.

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