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) {r €R:r+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) {r €R:r+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:**Problem 4: Determining Open and Closed Sets**
For each set, 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 within the set. If a set is not closed, find a limit point that is not contained in the set.
**Sets to Evaluate:**
(a) \( \mathbb{Q} \) (The set of rational numbers)
(b) \( \mathbb{N} \) (The set of natural numbers)
(c) \( \{ x \in \mathbb{R} : x \neq 0 \} \) (The set of all non-zero real numbers)
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