[ View Follow Ups ] [ Post Followup ] [ Back to the Course Discussion List ] [ Help ]

Sets, Maps and Symmetry Groups Course Discussion List


Re: Continuous functions on disconnected sets?

Posted by Daniel Goroff on November 28, 1999 at 21:06:23:

In Reply to: Continuous functions on disconnected sets? posted by David Molnar on November 27, 1999 at 15:18:34:


Glad to hear other opinions and examples concerning this question. When in doubt, always go back to the definitions. Is your example
continuous at each point in its domain? Did any of our approaches to continuity mention domain restrictions?

The Connected Image Theorem does say that the the image of a connected set under a continous map must be connected. If, as your second example suggests, some given function has an image that is not connected, does it or does it not necessarily follow that the function is discontinuous?

Imagine taking the real line with the discrete topology rather than the standard Euclidean one. Is it connected? What about continuous functions on this space?

Follow Ups:


Post a Followup

Name    : 
E-Mail  : 
Subject : 
Comments:


[ View Follow Ups ] [ Post Followup ] [ Back to the Course Discussion List ] [ HELP ]


This discussion list is provided by The Instructional Computing Group (ICG) of FAS Computer Services

Copyright © The President and Fellows of Harvard College