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1) Is an infinite intersection of open sets not open?

2) Is an infinite union of closed sets not closed?

3)But an infinite union of open sets is open.

4) And an infinite intesection of closed sets is closed.

This information is all correct?

If so could you provide reasoning to them especially the first two?

For 1) Is it because an infinite intersection of open sets could be a single point. This set which contains only a single point and so there is no 'ball' that can be drawn in this set with a non zero radius with the point as its centre. Since that point is the whole set.

But I have been too specific there may be cases where the infinite intesection may contain more than 1 point.

2) Is an infinite union of closed sets not closed?

3)But an infinite union of open sets is open.

4) And an infinite intesection of closed sets is closed.

This information is all correct?

If so could you provide reasoning to them especially the first two?

For 1) Is it because an infinite intersection of open sets could be a single point. This set which contains only a single point and so there is no 'ball' that can be drawn in this set with a non zero radius with the point as its centre. Since that point is the whole set.

But I have been too specific there may be cases where the infinite intesection may contain more than 1 point.

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