Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


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

Topic: Topology & Sigma Algebra
Replies: 6   Last Post: Jun 21, 2013 11:52 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
FredJeffries@gmail.com

Posts: 1,022
Registered: 11/29/07
Re: Topology & Sigma Algebra
Posted: Jun 20, 2013 10:57 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Jun 20, 7:25 am, agapito6...@aol.com wrote:
> On Wednesday, June 19, 2013 3:11:56 PM UTC-5, quasi wrote:
> > agapito6314 wrote:
>
> > >The Euclidean topology on R (E) is that generated by the
>
> > >open intervals (x,y), closed under finite intersections and
>
> > >arbitrary unions.
>
> > >The Borel sigma algebra (B) also generated by the open
>
> > >intervals, is closed under complementation and countable
>
> > >intersections.
>
> > >It appears as if some subsets of R are included in one and
>
> > >not the other.  Is that the case?  If so, can someone please
>
> > >supply examples of a set in E and not in B, and vice versa.
>
> > First, note that E doesn't need arbitrary unions -- countable
>
> > unions suffice (every open interval contains a rational
>
> > number).
>
> > Also B gets countable unions via DeMorgan's law, hence B
>
> > contains all open sets.
>
> > Thus, E is a subset of B.
>
> > However B contains sets which not open, hence not in E, for
>
> > example [0,1].
>
> > quasi
>
> Thanks.  Is B, in fact, the power set of R? If not, what elements of the power set would be missing from B?


https://en.wikipedia.org/wiki/Borel_set#Non-Borel_sets



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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.