Intrersection of open set is closed
In the first chapter of Probability wih Martingales (Willams) I came
across the following relation
$$(-\infty,x]=\bigcap_{n\in N}(-\infty,\, x+n^{-1}).$$ Even though this is
intuitive to me I would like to know if this is a rigorous statement. Is
the intersection of a infinite number of sets defined in the same way as
for a countable number of sets ? or by some limiting operation like liminf
or limsup?
Thank you.
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