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Dragonfinity · 2005 February 17th, 01:32 AM

The image of a connected subset under a continuous map is connected. The set (0,1) is connected, so its image S is connected. However, the image of an open set is not necessarily open. For example, if f is any constant function, then S is merely one point, which is a closed set.

2005 February 17th, 01:32 AM	#2 (permalink)
Dragonfinity Socratic realist Join Date: Feb 2005 Location: Georgia, USA Posts: 220	Re: Open vs. connected subsets The image of a connected subset under a continuous map is connected. The set (0,1) is connected, so its image S is connected. However, the image of an open set is not necessarily open. For example, if f is any constant function, then S is merely one point, which is a closed set.