Timeline for What does the property that path-connectedness implies arc-connectedness imply?
Current License: CC BY-SA 2.5
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| May 25, 2010 at 9:27 | comment | added | KP Hart | The best I can come up with then is an artificial ``any two points are connected by a locally connected metric continuum''. Any arc is such a continuum and the exercise mentioned above establishes that such continua are arcwise connected. It looks to me like that exercise, a step towards the Hahn-Mazurkiewicz theorem, will have to be a main part of any argument and any iff-condition that should set things up for a construction of an arc will be as artificial as what I wrote above. | |
| May 24, 2010 at 3:13 | comment | added | skupers | But it is not necessary. The real line with a double origin is a counterexample. | |
| May 21, 2010 at 12:59 | history | answered | KP Hart | CC BY-SA 2.5 |