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: definition of closure in topological space question
Replies: 11   Last Post: Nov 20, 2012 3:46 PM

Advanced Search

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

Posts: 254
Registered: 4/30/07
Re: definition of closure in topological space question
Posted: Nov 20, 2012 3:46 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Thank you everyone for your replies to this post :)

-- OP

On Saturday, November 17, 2012 6:10:00 PM UTC+8, Daniel J. Greenhoe wrote:
> Closure in topological space is defined using at least two different ways in the literature:
>
> 1. cl(A) is the intersection of all closed sets containing A.
>
> 2. cl(A) is the intersection of all neighborhoods containing A, where a neighborhood is any set containing an open set (an element of the topology).
>
>
>
> Examples of authors who use 1 include Kelley, Munkres, Thron, and McCarty.
>
> Examples of authors who use 2 include Mendelson and Aliprantis & Burkinshaw.
>
>
>
> My question is, one definition considered to be more "standard" than the other (from my very limited survey, 1 might seem more standard).
>
>
>
> Aliprantis/Burkinshaw hints that 2 is influenced by metric space theory.
>
>
>
> I might guess that there are other definitions possible (hence the "Kuratowski closure axioms"?)
>
>
>
> Pointers to good references are especially appreciated.
>
>
>
> Many thanks in advance,
>
> Dan





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.