Timeline for Base of topology for metric-like space
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
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| Dec 29, 2017 at 9:39 | comment | added | Pietro Majer | An analogous notion is the "mountain distance", a function $q(x,y)$ that shares all properties of a distance but symmetry (one example is the Hausdorff half-distance). Of course one can make a true distance just symmetrizing it, $q(x,y)+q(y,x).$ The point is whether we really need to give these objects a name. | |
| Dec 13, 2017 at 6:24 | comment | added | Martin Sleziak | BTW mentioning where you have taken the definitions in your question (metric-like, $B(x,\varepsilon)$ from would be, in my opinion, an improvement to the question. (A reasonable guess might be the paper I found in Google Scholar, but it is still just a guess.) | |
| Dec 12, 2017 at 6:30 | review | Close votes | |||
| Dec 12, 2017 at 20:27 | |||||
| Dec 11, 2017 at 16:53 | comment | added | Martin Sleziak | You can find links to some basic info about comment replies, for example, here. (In particular, they do not work if you add space after the @.) | |
| Dec 11, 2017 at 16:52 | answer | added | Martin Sleziak | timeline score: 3 | |
| Dec 11, 2017 at 16:11 | comment | added | youssef sabar | @ Martin Sleziak,the definition of open ball is not same | |
| Dec 11, 2017 at 1:04 | comment | added | Yemon Choi | @MartinSleziak I have cast the final vote to reopen, so that you can put some of the details from your earlier comments into an answer below | |
| Dec 11, 2017 at 1:03 | history | reopened |
Will Brian Stefan Kohl♦ Arturo Magidin Ramiro de la Vega Yemon Choi |
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| Dec 8, 2017 at 22:18 | comment | added | Martin Sleziak | @WillBrian Since it seems that you are a bit interested in the question (you mentioned that you voted that reopen), I wanted to let you know that I have posted the question (with some additional context) on another site: Does metric-like space generate a topology? | |
| Dec 7, 2017 at 1:00 | comment | added | Martin Sleziak | It seems that Wikipedia calls this a metametric. A reference given there is Väisälä, Jussi (2005), "Gromov hyperbolic spaces", Expositiones Mathematicae, 23 (3): 187–231, doi: 10.1016/j.exmath.2005.01.010. From this paper: "A metametric space is metrizable. In fact, a metametric $d$ can be changed to a metric $d_1$ simply by setting $d(x,x)=0$ and $d_1(x,y)=d{x,y}$ for $x\ne y$. Then $d$ and $d_1$ define the same topology." | |
| Dec 6, 2017 at 20:09 | history | rollback | youssef sabar |
Rollback to Revision 3 - I think is very interesting question
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| Dec 6, 2017 at 19:54 | comment | added | youssef sabar | @ Arturo Magidin, does not reearch-level questions?!! | |
| Dec 6, 2017 at 18:10 | review | Reopen votes | |||
| Dec 7, 2017 at 11:57 | |||||
| Dec 6, 2017 at 18:02 | comment | added | Martin Sleziak | @WillBrian As a follow-up to your edit I have also corrected a few minor typos and explicitly added to the post that this is different from metric space. (Since this can be missed if somebody does not read carefully.) A quick Google search leads to the paper A. Amini-Harand: Metric-like spaces, partial metric spaces and fixed points, doi.org/10.1186/1687-1812-2012-204. | |
| Dec 6, 2017 at 17:59 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
minor typo
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| Dec 6, 2017 at 17:53 | history | edited | Martin Sleziak | CC BY-SA 3.0 |
minor typo
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| Dec 6, 2017 at 17:51 | history | edited | Will Brian | CC BY-SA 3.0 |
edited body
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| Dec 6, 2017 at 17:50 | comment | added | Will Brian | There is a typo in the question that makes it difficult to understand what is being asked, but if one replaces the $d$'s with $p$'s in the bottom part of the question, then an interesting question emerges. (@youssef: I think, but I'll have to check details, that the answer is no in general, but yes if $p$ is continuous.) I'm voting to reopen. | |
| Dec 6, 2017 at 16:36 | history | closed |
Arturo Magidin Mark Grant Asaf Karagila♦ Gro-Tsen R W |
Not suitable for this site | |
| Dec 6, 2017 at 15:55 | review | Close votes | |||
| Dec 6, 2017 at 16:41 | |||||
| Dec 6, 2017 at 15:28 | review | First posts | |||
| Dec 6, 2017 at 15:36 | |||||
| Dec 6, 2017 at 15:25 | history | asked | youssef sabar | CC BY-SA 3.0 |