Timeline for Construct a topologically $\infty$-dimensional separable metric space.
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Feb 10, 2014 at 17:09 | history | edited | user9072 |
edited tags
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| Feb 17, 2013 at 9:52 | comment | added | Włodzimierz Holsztyński | Andrey, you're welcome to edit my question (that's what I meant in my earlier comment, just under yours).) | |
| Feb 16, 2013 at 22:43 | comment | added | Włodzimierz Holsztyński | I see TeX+HTML problems in my comment above. I think that Hilbert Space can be disconnected by a closed subset which does not contain any arc. | |
| Feb 16, 2013 at 22:41 | comment | added | Włodzimierz Holsztyński | I feel that it should not be difficult to disconnect $\el^2$ by a closed subset which does not contain any topological arc (any subspace homeomorphic to $I$). I may come back to this later. | |
| Feb 16, 2013 at 16:45 | comment | added | Gerald Edgar | Do we know that Hilbert space $l^2$ is not such a space? Explain, please. | |
| Feb 16, 2013 at 9:36 | comment | added | Włodzimierz Holsztyński | @A.B.--please (be my guest :-) | |
| Feb 16, 2013 at 9:25 | comment | added | Andrej Bauer | May I edit the question a bit? You can always cancel the changes if you do not like that. | |
| Feb 16, 2013 at 9:06 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
extra info
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| Feb 16, 2013 at 9:00 | comment | added | Włodzimierz Holsztyński | @A.B.--my bad. Any space $X$, which satisfies the above 2 conditions (from the question) must be $\infty$-dimensional--think of the Ind definition of the topological dimension. (The bad luck wants that my first attempt at posting my question ended in a failure; I've encountered a software system difficulty. My first edition was quite extensive. It's hard for me to concentrate on the second edition, when I am a kind of sick of writing about the same again). | |
| Feb 16, 2013 at 7:49 | comment | added | Andrej Bauer | Oops, I was reading the second condition wrong, thinking you want a copy of $X$ inside $X \setminus A$. $I^\omega$ obviously is not a solution. | |
| Feb 16, 2013 at 7:47 | comment | added | Andrej Bauer | I find this question very confusingly written. In the title you say "$\infty$-dimensional" but not in the text. If infinite dimension is a consequence of your conditions, please indicate that. The text is fragmented (what is the first paragraph for?). You could just say "fixed-point property" in the single place where you use "fpp", so you don't have to explain what the acronym means. Also, it might help if you explain why $I^\omega$ isn't a solution, even if so for a trivial reason. | |
| Feb 16, 2013 at 7:29 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
a terminological explanation added
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| Feb 16, 2013 at 7:26 | comment | added | Włodzimierz Holsztyński | fpp = the Fixed Point Property (I'll add this explanation to the formulation of the problem). | |
| Feb 16, 2013 at 6:30 | comment | added | Mariano Suárez-Álvarez | What's fpp? ${}$ | |
| Feb 16, 2013 at 6:23 | history | asked | Włodzimierz Holsztyński | CC BY-SA 3.0 |