Let R` be the set of real numbers with the lower limit topology (the collection of the intervals [a, b) is the basis). (a) Show that the interval (1, 6) is open in R`. (b) What can you say about the interval (1, 6]? Justify your answer. (c) What about the interval (−∞, 3)?
Let R` be the set of real numbers with the lower limit topology (the collection of the intervals [a, b) is the basis). (a) Show that the interval (1, 6) is open in R`. (b) What can you say about the interval (1, 6]? Justify your answer. (c) What about the interval (−∞, 3)?
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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Let R` be the set of real numbers with the lower limit topology
(the collection of the intervals [a, b) is the basis).
(a) Show that the interval (1, 6) is open in R`.
(b) What can you say about the interval (1, 6]? Justify your answer.
(c) What about the interval (−∞, 3)?
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