Solucija - Is there a natural topology on the set of open sets?

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Is there a natural topology on the set of open sets?

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Do you need topology or algebra to come to a conclusion about the cardinality of a set? Yahoo! Answers

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So, if there is an infinite set I and it is described as a set of sets, what can we say about the nature of all element sets--they all can be open or all have to be closed or some have to be both? Quora