Timeline for A question about continuous mappings
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| May 27, 2011 at 10:03 | comment | added | Sergey Melikhov | Pietro: sorry, I misread your answer. I now deleted mine. For the record: 1) A specific closed connected subset of the plane that is not path connected is the topologist's sine curve. 2) Your argument shows that a locally compact space is a continuous proper image of the real line if and only if it is separable, metrizable, connected and locally connected. 3) A related characterization is, a space is a continuous open image of the Baire space (=the subspace of the real line consisting of irrational numbers) if and only if it is Polish (=separable and metrizable by complete metric). | |
| May 26, 2011 at 7:29 | history | edited | Pietro Majer | CC BY-SA 3.0 |
edited body
|
| May 26, 2011 at 7:24 | history | edited | Pietro Majer | CC BY-SA 3.0 |
added 1329 characters in body; added 1 characters in body
|
| May 25, 2011 at 20:30 | comment | added | Pietro Majer | However if it is also closed I think that you can make a construction à la Peano, producing a single arc that connects all points. | |
| May 25, 2011 at 20:25 | history | edited | Pietro Majer | CC BY-SA 3.0 |
added 149 characters in body
|
| May 25, 2011 at 20:11 | history | edited | Pietro Majer | CC BY-SA 3.0 |
added 793 characters in body
|
| May 25, 2011 at 19:18 | comment | added | Garabed Gulbenkian | Thanks, Pietro for your answer which makes me feel stupid for not having thought of it myself. If I modify my second question by asking whether every arcwise connected subset of a finite-dimensional Euclidean space is a continuous image of L, I still suspect that the answer would be "no". | |
| May 24, 2011 at 18:03 | history | answered | Pietro Majer | CC BY-SA 3.0 |