Drexel dragonThe Math ForumDonate to the Math Forum


Math Forum
 Ask Dr. Math
 Discussions
 Internet Newsletter
 MathTools
 Problems of the Week
 Teacher2Teacher
 Teacher Exchange
 Workshops

Search All of the Math Forum:
Browse our Internet Mathematics Library

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: Compactification
Replies: 15   Last Post: Mar 17, 2013 6:11 AM

Advanced Search
Reply to this Topic Reply to this Topic

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

Posts: 603
Registered: 1/8/12
Compactification
Posted: Dec 11, 2012 11:13 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

(h,Y is a (Hausdorff) compactification of X when h:X -> Y is an embedding,
Y is a compact (Hausdorff) space and h(X) is a dense subset of Y.

Why the extra luggage of the embedding for the definition of
compactification? Why isn't the definition simply
Y is a compactification of X when there's some
embedding h:X -> Y for which h(X) is a dense subset of Y?

I see no advantage to the first definition. The second definition
has the advantage of being simpler and more intuitive. So why is
it that the first is used in preference to the second which I've
seen used only in regards to one point compactifications?

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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2013. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.