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Unformatted text preview: Show that if X is an inﬁnite set, it is connected in the topology J = { A : X \ A is ﬁnite or all of X } . Problem 6. Is the space R l connected? Problem 7. Is the product of path connected spaces is path connected? Problem 8. If A is a connected subset of X , is the interior of A is connected? Does the converse hold? Problem 9. Show that if U is open path connected subset of R 2 then U is path connected. Hint: Show that given X ∈ U , the set of points x ∈ U that can be joined to x by a path in U is both open and closed. 1...
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This note was uploaded on 11/14/2011 for the course MATH 367 taught by Professor Sdd during the Spring '11 term at Middle East Technical University.
 Spring '11
 sdd
 Math, Topology

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