Re: intersections and unions in the definition of a topology

On 2005-06-10, bode@xxxxxxxxxxxxx <bode@xxxxxxxxxxxxx> wrote:
> I have a rather simple question regarding the definition of a topology:
>
> Why are there allowed to be arbitrary unions of open sets in a
> topology, but only finite intersections of open sets? It seems to be a
> rather subtle distinction, so I wonder why is a topology not arbitrary
> unions and arbitrary intersections, or finite unions and finite
> intersections, or even finite unions and arbitrary intersections. I
> would greatly appreciate an answer to this question; it's been bugging
> me for a while.

Note that your last alternative, closed under finite union and arbitrary
intersection, is simply the dual way of defining a topological space by
specifying its closed sets, so not different at all.

--
fiesh
.

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