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Unformatted text preview: , 1 } be a function. Show that X is connected if and only if the only continuous f are constant functions. (8) A space X is called path connected if for every x,y X , there is a continuous function : [0 , 1] X with (0) = x and (1) = y ( is a path or curve connecting x and y ). Show that if a space is path connected, then it is connected. (9) If we lay out an accurate map of California on the oor of our classroom, prove that exactly one point on the map lies directly over the place in California it represents. (10) Let x > 0 and x n +1 = 1 1+ x n . Use the xed point theorem to prove that the sequence { x n } converges and then nd its limit. 1...
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This note was uploaded on 05/04/2011 for the course MATH 73 taught by Professor Danberwick during the Spring '09 term at University of California, Berkeley.
 Spring '09
 DANBERWICK
 Division, Sets

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