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1. • CommentRowNumber1.
   • CommentAuthorporton
   • CommentTimeMar 9th 2014
   • (edited Mar 10th 2014)
   • PermaLink
   Author: porton
   Format: MarkdownItexIn <a href="http://ncatlab.org/nlab/show/proximity+space">proximity+space article</a> $A \ll B$ is defined as $(X \setminus A)\;\delta\;B$. But in <a href="https://en.wikipedia.org/wiki/Proximity_space">Wikipedia</a> it is defined as "$A \delta X-B$ is false". What is the right notation? Where is the error?

   In proximity+space article $A \ll B$ is defined as $(X \setminus A)\;\delta\;B$.

   But in Wikipedia it is defined as “$A \delta X-B$ is false”.

   What is the right notation? Where is the error?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeMar 10th 2014
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI think Wikipedia is right on this one, our page must have a typo.

   I think Wikipedia is right on this one, our page must have a typo.

3. • CommentRowNumber3.
   • CommentAuthorporton
   • CommentTimeMar 10th 2014
   • (edited Mar 10th 2014)
   • PermaLink
   Author: porton
   Format: MarkdownItex[Ignore this my comment. It is erroneous.] Then the sets of the form $\bigcup_{i \in n} ( A_i \times A_i)$ contain empty set (and thus is not a base for a uniformity) because $A_i=\emptyset$ is allowed (for every possible $B_k$). So there must be at least one more error in <a href="http://ncatlab.org/nlab/show/proximity+space">proximity+space</a> article. Maybe $B_k \ll A_k$ is confused with $A_k \ll B_k$?

   [Ignore this my comment. It is erroneous.]

   Then the sets of the form $\bigcup_{i \in n} ( A_i \times A_i)$ contain empty set (and thus is not a base for a uniformity) because $A_i=\emptyset$ is allowed (for every possible $B_k$).

   So there must be at least one more error in proximity+space article. Maybe $B_k \ll A_k$ is confused with $A_k \ll B_k$?

4. • CommentRowNumber4.
   • CommentAuthorporton
   • CommentTimeMar 10th 2014
   • PermaLink
   Author: porton
   Format: MarkdownItexI've edited our wiki to be the same as Wikipedia.

   I’ve edited our wiki to be the same as Wikipedia.