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

Topic: Onto [0,1]
Replies: 40   Last Post: Apr 29, 2013 10:16 PM

Advanced Search

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

Posts: 10,257
Registered: 7/15/05
Re: Onto [0,1]
Posted: Apr 25, 2013 5:54 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Butch Malahide wrote:
>quasi wrote:
>>
>> If X,Y are subsets of R, and f: X -> Y is a monotonic function,
>> then f is continuous (with respect to the relative topologies
>> on X and Y inherited from R).

>
>Hmm. Suppose X = [0,1] and Y = [0,1) union {2}. Let f: X -> Y
>be an order-preserving bijection, e.g., f(x) = x for x in [0,1),
>f(1) = 2. I don't believe that f is continuous with respect to
>the relative topologies on X and Y inherited from R. For one
>thing, X is compact and connected, while Y is neither. (I guess
>that was two things.) I guess you left out some assumptions.


Yes, I realized as much myself.

In fact, the immediate counterexample that ocurred to me was
very similar to the one you gave above.

All in all, my claim was pretty silly.

quasi



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.