Unformatted text preview: yd  ) = 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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 Spring '05
 SMITH
 Math, Topology, Metric space, Euclidean space, real line, Munkres §13, Munkres §16

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