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i have a clarification question:

if i have a metrizable space, can any open set be written as acountableunion of basis elts?

if not, can it have some properties that make this assertion true, like being T1 or sth like that.

thanks a lot.

just to clarify why i think so, i have a space X with a topology T on it.

Let's say this topology is metrizable, with a metric d. Then, the open sets O(x,r) = {y in X , d(x,y)<r} form a basis for this topology. so any elt in this topology, t in T can be written as a countable union of such O's.

I just want to know if this is works.

thx.

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# Metrizable space

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