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Re: Property related to denseness
Posted:
Jan 15, 2013 1:53 PM


In article <a1044dfe77d845e89f6f307894d02c86@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 <d2c170e4b59b4c738a7324374fc8b6e1@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 #include <Standard_Disclaimer> Visualize whirled peas!



