Consider X = [1,2]? with the relation (x1, y1)~(x2, Y2) if x1Y2 = x2y1. Also define 3x g: X → [1,2] by the rule g(x, y) = x+y c) Show that g is constant on equivalence classes of ~. d) Show that {[(x, y)]: (x, y) E X} and [1,2] are homeomorphir

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Consider X = [1,2]2 with the relation (x1, y1)~(x2, Y2) if x,y2 = x,y1. Also define
3x
g: X → [1,2] by the rule g(x, y) =
x+y'
c) Show that g is constant on equivalence classes of .
d) Show that {[(x, y)]: (x, y) E X} and [1,2] are homeomorphir
Transcribed Image Text:Consider X = [1,2]2 with the relation (x1, y1)~(x2, Y2) if x,y2 = x,y1. Also define 3x g: X → [1,2] by the rule g(x, y) = x+y' c) Show that g is constant on equivalence classes of . d) Show that {[(x, y)]: (x, y) E X} and [1,2] are homeomorphir
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