Wikipedia: History of Connectedness

Difference (from prior major revision) (minor diff, author diff)

Removed: 5,6d4

The connected (or path-connected) subsets of the real numbers R are called intervals.

Added: 9a8,13

However, subsets of R are connected if and only if they are path-connected.
These subsets are the intervals of R.

If X and Y are topological spaces, f : X -> Y is continuous, and X is connected (respectively, path-connected), then f(X) is connected (respectively, path-connected).
The intermediate value theorem can be considered as a special case of this result.

	Revision 9 . . (edit) December 7, 2001 5:18 am by Zundark [minor rewording]
	Revision 8 . . December 7, 2001 3:35 am by Zundark [also reference intermediate value theorem]
	Revision 7 . . December 7, 2001 2:48 am by Zundark [link to Interval]
	Revision 6 . . August 31, 2001 6:29 pm by Zundark [topologist's sine curve]