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Unformatted text preview: y-d | ) = s } of side length 2 s > . 4. (a) Show that the intervals (0 , 1) and (0 , 2) are not isometric. (b) Show that R and (0 , 1) are not isometric. (c) Show that R and (0 , ) are not isometric. 5. Show that a triangle and a square in R 2 are not isometric. ( Note: You should consider an arbitrary triangle and an arbitrary square, rather than picking their sidelengths yourself. Also, when I say triangle and square, I mean their boundaries, not their interiors.) Challenge (extra credit): Show that [0 , 1] Q and (0 , 1) Q are homeomorphic. Note: We will see later in the course that [0 , 1] and (0 , 1) are not homeomorphic....
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This note was uploaded on 02/10/2010 for the course MATH 205 taught by Professor Smith during the Spring '05 term at Adrian College.
- Spring '05