- #1

jem05

- 56

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hello,

i have a clarification question:

if i have a metrizable space, can any open set be written as a

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.

i have a clarification question:

if i have a metrizable space, can any open set be written as a

**countable**union 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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