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2) Show that the interval (2, 4) is open in the upper limit topology on R. [Hint: Express (2, 4) as a union of basis elements for the upper limit topology.

2) Show that the interval (2, 4) is open in the upper limit topology on R. [Hint: Express (2, 4) as a union of basis elements for the upper limit topology.

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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show the interval

(a, b) = {x E R|a < x < b}; [a, b) = {x E R|a <x <b}; (a, b] = {x ER la < x < b} and [a, b] = {x € R[a <x< b}
Transcribed Image Text:(a, b) = {x E R|a < x < b}; [a, b) = {x E R|a <x <b}; (a, b] = {x ER la < x < b} and [a, b] = {x € R[a <x< b}
2) Show that the interval (2, 4) is open in the upper limit topology on R. [Hint: Express (2, 4) as a union of basis elements for the upper limit topology.
Transcribed Image Text:2) Show that the interval (2, 4) is open in the upper limit topology on R. [Hint: Express (2, 4) as a union of basis elements for the upper limit topology.
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