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Re: Property related to denseness
Posted:
Jan 16, 2013 4:34 PM


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.



