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Problem 3.24. Let X = [0, 1]U{2} C R. On the one hand, X has a subspace topology Ti induced by the standard (order) topology on R. On the other hand, X has a natural order induced by the natural order on R. This order induces an order topology T2 on X. (1) How are T1 and T2 related? (2) Is 1 a limit point of X? (3) Is 2 a limit point of X?

Problem 3.24. Let X = [0, 1]U{2} C R. On the one hand, X has a subspace topology Ti induced by the standard (order) topology on R. On the other hand, X has a natural order induced by the natural order on R. This order induces an order topology T2 on X. (1) How are T1 and T2 related? (2) Is 1 a limit point of X? (3) Is 2 a limit point of X?

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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Solve 3.24 in detail please.

I have posted this on chegg and got the wrong answer so please don't copy and paste it from chegg , otherwise I will have to report u.

 

Problem 3.24. Let X = [0, 1] U {2} C R. On the one hand, X has a subspace topology Ti induced by the standard (order) topology on R. On the other hand, X has a natural order induced by the natural order on R. This order induces an order topology T2 on X. (1) How are T1 and T2 related? (2) Is 1 a limit point of X? (3) Is 2 a limit point of X ? Problem 3.25. Redo Problem 3.24 with X = [0, 1) U {2}..
Transcribed Image Text:Problem 3.24. Let X = [0, 1] U {2} C R. On the one hand, X has a subspace topology Ti induced by the standard (order) topology on R. On the other hand, X has a natural order induced by the natural order on R. This order induces an order topology T2 on X. (1) How are T1 and T2 related? (2) Is 1 a limit point of X? (3) Is 2 a limit point of X ? Problem 3.25. Redo Problem 3.24 with X = [0, 1) U {2}..
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