Timeline for Stronger form of connectedness than path-connectedness
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Mar 31, 2016 at 14:49 | vote | accept | Dominic van der Zypen | ||
| Mar 31, 2016 at 14:48 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 83 characters in body
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| Mar 31, 2016 at 14:36 | comment | added | Dominic van der Zypen | Right, the one-space example... I changed the question a bit to evade this example | |
| Mar 31, 2016 at 14:35 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
added 3 characters in body
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| Mar 31, 2016 at 12:48 | answer | added | Gro-Tsen | timeline score: 5 | |
| Mar 31, 2016 at 12:21 | comment | added | Simon Henry | ... and obviously it will also implies that you don't have many $C$-connected spaces: a functionally separated space will always be "$C$ totally disconected". | |
| Mar 31, 2016 at 12:12 | comment | added | Simon Henry | More seriously, unless I'm mistaken, If $C$ is not functionally separated (more precisely if $c_0$ and $c_1$ cannot be separated by continuous functions) then $[0,1]$ is not going to be $C$-connected and conversely if $C$ is functionally separated then every path connected space will be $C$-connected. So you are looking for examples of path-connected non functionally separated spaces. Lots of non Hausdorff example, and I'm sure books like "counterexamples in topology" contains lots of Hausdorff examples. | |
| Mar 31, 2016 at 12:01 | comment | added | Simon Henry | $(\{*\},*,*)$ ?. | |
| Mar 31, 2016 at 12:00 | history | edited | Dominic van der Zypen | CC BY-SA 3.0 |
Fixed grammar
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| Mar 31, 2016 at 11:55 | history | asked | Dominic van der Zypen | CC BY-SA 3.0 |