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Question: Let X = R For the given set determine whether or n...

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Let X = R For the given set determine whether or not the set is open in TU usual topology, TH half - open interval topology, TC open half - line topology, TD discrete topology, TI indiscrete topology, TF finite complement topology, or TCC countable complement topology. List only the topologies where it is OPEN; You do not have to justify your answer.

(a) (1, 5]

(b) Q

(c) R Q

(d) R Z

(e) {1/n : n Z+}

(f) R {1/n : n Z+}

(g) {1/n : n Z+} {0}

(h) R – ({1/n : n Z+} {0})

Explanation / Answer

(a)- R-Q is open because Q is closed.

(d)-   R-Z is open because Z is closed

  (f)- R-{1/n :n in Z+} is open because {1/n} is closed

(g)-   {1/n : n Z+} {0} is open

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