Exercise 3. Are the following subsets of the real line with its usual topology (in which U CR is open if and only if for every x € U there is € > 0 with (x − ¤, x + €) ≤ U) open, closed, both or neither? Explain. (1) [1,3); (2) (1,3) U (5, ∞); (3) (-∞, ∞); (4) { ½ : n € N} U {0}; (5) The set Q of rationals.
Exercise 3. Are the following subsets of the real line with its usual topology (in which U CR is open if and only if for every x € U there is € > 0 with (x − ¤, x + €) ≤ U) open, closed, both or neither? Explain. (1) [1,3); (2) (1,3) U (5, ∞); (3) (-∞, ∞); (4) { ½ : n € N} U {0}; (5) The set Q of rationals.
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:Exercise 3. Are the following subsets of the real line with its usual topology
(in which U CR is open if and only if for every x ‹ U there is € > 0 with
(x − €, x + € ) ≤ U) open, closed, both or neither? Explain.
(1) [1,3);
(2) (1,3) U (5,00);
(3) (-∞0, ∞0);
(4) { neN} U {0};
(5) The set Q of rationals.
.
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