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Topic: Property related to denseness
Replies: 8   Last Post: Jan 16, 2013 4:34 PM

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Michael Stemper

Posts: 671
Registered: 6/26/08
Re: Property related to denseness
Posted: Jan 15, 2013 1:53 PM
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In article <a1044dfe-77d8-45e8-9f6f-307894d02c86@u19g2000yqj.googlegroups.com>, Butch Malahide <fred.galvin@gmail.com> writes:
>On Jan 14, 12:55=A0pm, mstem...@walkabout.empros.com (Michael Stemper) wrote:
>> In article <d2c170e4-b59b-4c73-8a73-24374fc8b6e1@googlegroups.com>, Paul <pepste...@gmail.com> writes:

>> >Let A be a subset of the topological space of X.
>> >What is the standard terminology for the property
>> > that X =3D the intersection of all the open sets that contain A?

>> The trivial topology?
>> If these two Xs refer to the same thing, then I don't see how X could be
>> the intersection of more than one subset of X, and I don't see how that
>> subset could be anything other than X.

>Yes, the OP's property that "X =3D the intersection of all the open sets
>that contain A" could be stated more simply as "X is the only open set
>that contains A". This is, of course, a property of a subset A of a
>topological space X.

Okay, thanks for validating my thinking.

> By "the trivial topology" I guess you mean the
>"indiscrete" topology,

Willard also uses that term. It makes sense that if the finest topology
is called "discrete" that the coarsest could be called "indiscrete".

Michael F. Stemper
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