4. For each set determine whether the following sets are open, closed, or neither. If a set is not open, find a point in the set for which there is no E-neighborhood contained in the set. If a set is not closed, find a limit point'that is not contained in the set. (a) Q (b) N (c) {z ER:0}
4. For each set determine whether the following sets are open, closed, or neither. If a set is not open, find a point in the set for which there is no E-neighborhood contained in the set. If a set is not closed, find a limit point'that is not contained in the set. (a) Q (b) N (c) {z ER:0}
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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Transcribed Image Text:**Question 4: Set Openness and Closedness Analysis**
Determine whether the following sets are open, closed, or neither. If a set is not open, identify a point in the set for which there is no ε-neighborhood contained in the set. If a set is not closed, find a limit point that is not contained in the set.
(a) **Q** (the set of rational numbers)
(b) **N** (the set of natural numbers)
(c) **{x ∈ ℝ : x ≠ 0}** (the set of all real numbers except zero)
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