The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Property related to denseness
Posted: Jan 14, 2013 2:15 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jan 14, 12:55 pm, (Michael Stemper)
> In article <>, Paul <> writes:
> >Let A be a subset of the topological space of X.
> >What is the standard terminology for the property
> > that X = 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 = 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. By "the trivial topology" I guess you mean the
"indiscrete" topology, in which the only open sets are the empty set
and X itself? If X has the indiscrete topology, then every nonempty
subset A will have the OP's property. On the other hand, if X is a
topological space in which all one-point sets are closed (a so-called
T_1-space), then the OP's condition holds only for A = X.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.