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samiirah
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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
 one year ago
samiirah Group Title
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
 one year ago

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sralmai Group TitleBest ResponseYou've already chosen the best response.0
I 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.
 one year ago

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