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Martin Sleziak
Martin Sleziak
9:26 AM
The only answer posted so far suggests that my counterexample is indeed correct and also suggests modification which would make this counterexample not work.
> Interestingly the paper you cited mentions "partial metrics" directly in the introduction, with the triangle inequality being changed into $$\sigma(x,z) \leq \sigma(x,y) + \sigma(y,z) - \sigma(y,y)$$ which seems to be the right fix, making this trick impossible.
Seeing that this paper is widely cited (Google Scholar, citations), I wonder whether this was just a slip up which is corrected later. Or whether some of the follow-up papers simply continue with incorrect definition
No problems are mentioned in Zentralblatt.
I do not have access to the MathSciNet review.
I suppose somebody working in fixed-point theory might probably be able to judge this, since most citations seem to be from this area.
 
 
1 hour later…
Martin Sleziak
Martin Sleziak
10:46 AM
I will add to the vincenzoml's inquiry that there are also some posts on the main related to this:
-1
Q: paths in cech closure spaces

vincenzomlI'm trying to define a notion of path in Cech closure spaces that specialises to paths in topology and to "graph-like" paths in quasi-discrete closure spaces (that is, those where the closure of any set is the union of the closure of its singletons, or equivalently, those generated by a set $X$ a...

general-topology
-1
Q: open-ended paths in topology

vincenzomlIn topology, paths are always defined as images of continuous functions from the unit interval $I$. However, it also makes sense to define "open ended" paths, e.g. as continuous functions from the real line $R$ to a space. And furthermore, the image of any continuous $f : I \to X$ is also the ima...

general-topology
Cech closure space means a space with Čech closure operator?
 

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