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In the section on pseudoquasimetric spaces, the wording currently seems to imply that the category of non-extended pseudoquasimetric spaces still admits all finite coproducts, just not infinite ones. Isn't that false? The distance between elements of X and Y in X+Y would have to be infinite in order
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Hi! The definition of the metric is false (btw it is also false on the page for distance). What you are defining is a pseudometric when we only request d(x,x) = 0 (which is defined correctly later on in the section on generalizations). A distance has to satisfy the stronger condition that d(x,y) = 0
313:
The SNCF and the post office metric are two distinct concepts. The distance between
Marseille and Lyon with respect to the SNCF metric is just the Euclidian distance bewtween the two cities, whereas it is the sum of the Euclidian distances Marseille-Paris and Lyon-Paris with respect to the post
261:
on MathOverFlow. Namely, if we collapse (to a point) each closed interval complementary to the Cantor set, then the topological quotient space is homeomorphic to , but the pseudometric defined in the article is trivial (all distances are 0).
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FWIW, I would prefer to go back to four axioms, even if they are redundant. It's a very small point, but I believe explicitly stating non-negativity early on really helps the reader on their first encounter with the definition. –
949:
This section talks about relaxing axioms 1 to 4, but there are only 3, as they've been refactored. I don't think I know how to correct it, given that removing eg 2 or 3 may mean you have to add positivity back in.
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for X+Y to admit nonexpansive maps to all spaces X and Y map to, but that's not possible with a non-extended metric, so for any two nonempty spaces there should not be a coproduct at all.
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The image provided seems to suggest that the diameter of a bounded set is the diameter of the smallest ball which contains it, which is incorrect (e.g. in
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That definition is for a closed ball - it includes points on the boundary, at distance r. For an open ball, you need all points less than distance r.
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The blue table of contents overwrites the black text a long ways down the page, making the text very hard to read. Can the format be changed?
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as models of what to work towards. "Group" is a featured article and the other two are officially Good
Articles. --
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0, the open ball of radius r around x is defined to be the set of points that are at most distance r from x:
871:(the link 'Upload a new version of this file' in the 'File history' section, below the table of versions). --
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The best way IMHO will be preparing a correct image without a circle and uploading it as a newer version at
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I'm currently working on merging the two as well as rewriting this article. There's a discussion at
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Or rather I should say that it is a very weird /unconventional way of doing it since 1+2 =: -->
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to remove explicit reference to the number of axioms. Please check that I didn't mess it up.
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Knowledge talk:WikiProject
Mathematics#Metric space and Metric (mathematics)
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I don't have the capacity to do that easily on my device, unfortunately.
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I have noticed that this page does not provide any link to the page
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For any point x in a metric space M and any real number r : -->
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on 4 December 2005 at 18:07. He is not active since Oct 2012.
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https://archiveofourown.org/works/777002/chapters/11228542
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106:This article is within the scope of
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1021:Link to page "Metric (mathematics)"
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502:, so every sequence of points from
49:It is of interest to the following
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685:(or both), so any limit point of
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
