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Unformatted text preview: continuous. 3.3.3 Exercise: #4,8 Recommended: #3,6,10 #3 is shortanswer; a rigorous proof is not required. 1. If F is closed and K is compact, then F K is compact. 58 Math 413 Topology of the Real Line 2. Suppose K = { K } is a collection of compact sets. if K has the property that the intersection of every nite subcollection is nonempty, then prove that T K is nonempty. (Try contradiction or DeMorgans.) 3. Suppose that every point of the nonempty closed set A is a limit point of A . Show that A is uncountable. (Try contradiction, and use the previous problem.)...
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This note was uploaded on 11/26/2011 for the course MAT 4944 taught by Professor Wong during the Fall '11 term at FSU.
 Fall '11
 Wong
 Sets

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