270 LIMITS AND OPEN SETS [12] a) {(x, y) : -1 < x < +1, y = 0}, c) {(x. v) : x + y' = 1}, b) {(x, y) : x and y are integers}, d) {(x, y) : x + y < 1}, e) {(x, r) : x = 0 or y = 0}.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Also, which of those 5 sets are compact?

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For each of the following subsets of the plane, draw the set, state whether it is open,
closed, or neither, and justify your answer in a word or two:
12.21
270
LIMITS AND OPEN SETS [1 2]
a) {(x, y') : -1 < x < +1, y = 0},
c) {(x, v) : x + y' = 1},
e) {x, y') : x = 0 or y = 0}.
b) {(x, y) : x and y are integers},
d) {(x, y) : x + y < 1},
Transcribed Image Text:For each of the following subsets of the plane, draw the set, state whether it is open, closed, or neither, and justify your answer in a word or two: 12.21 270 LIMITS AND OPEN SETS [1 2] a) {(x, y') : -1 < x < +1, y = 0}, c) {(x, v) : x + y' = 1}, e) {x, y') : x = 0 or y = 0}. b) {(x, y) : x and y are integers}, d) {(x, y) : x + y < 1},
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