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Re: Property related to denseness
Posted:
Jan 16, 2013 4:34 PM
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On Jan 16, 5:17 am, quasi <qu...@null.set> wrote:
> [. . .]
> The terminologies
>
> "the trivial topology on X"
>
> "the indiscrete topology on X"
>
> are both accepted, but I think "the indiscrete topology" is the
> one more commonly used.
>
> Willard mentions both but favors "the trivial topology".
>
> Wikipedia has "the trivial topology" first
>
> <http://en.wikipedia.org/wiki/Trivial_topology>
>
> but indicates that "the indiscrete topology" is a perfectly
> acceptable alternate.
>
> Personally, I like "the trivial topology" better, but it's not
> a big deal either way.
No big deal if you're an AI. For us humans, there is a lot of
terminology to keep track of, and it is worthwhile to keep it as
natural and easy to remember as possible. Personally, I never had any
trouble remembering which of the two extremal topologies is "discrete"
and which is "indiscrete"; the words themselves are pretty good clues.
However, as far as I can see it's completely arbitrary which of those
two topologies is "trivial"; it's just another bit of jargon to
memorize.
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