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 one year ago
let F c X be another open set. Show that F n G is also open. Give an example where the intersection of an arbitrarily family of open sets may fails to open.
please do help
 one year ago
let F c X be another open set. Show that F n G is also open. Give an example where the intersection of an arbitrarily family of open sets may fails to open. please do help

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sralmai
 one year ago
Best ResponseYou've already chosen the best response.0I don't have your definition of G. (Assuming G c X is an open set.) You can directly apply the definition in this case. For the case of an intersection of a family of open sets, consider the family of open sets A where An = (infinity, 1/n) and the family of open sets B where Bn = (1/n, infinity). The intersection of all A and B is {0}, which is closed.

domu
 one year ago
Best ResponseYou've already chosen the best response.0Visually, consider the intersection of the Xaxis and Yaxis
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