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The revision of 20:44 26 August 2018 created an error which should be reverted: The definition of neat submanifold should require , not .
I plan to fix this but first I want to check the one reference that is given, and compare that to the more standard reference of Hirsch's book "Differential Topology".
I'm unfamiliar with what represents in this context. Is it the boundary of ? So the corrected version specifies these three things?
: includes its own boundary.
: the boundary of A lies wholly on the boundary of .
: doesn't intersect the boundary of anywhere except at its own boundary.
The last one would mean, for example, that a bounded area on the surface of a ball doesn't meet the condition, but a slice through the ball does.
If I've got that right, it would be nice to spell the three points out explicitly, for the benefit of people who are interested in the ideas but don't easily see them from the notation.
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of
mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join
the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
The revision of 20:44 26 August 2018 created an error which should be reverted: The definition of neat submanifold should require , not .
I plan to fix this but first I want to check the one reference that is given, and compare that to the more standard reference of Hirsch's book "Differential Topology".
I'm unfamiliar with what represents in this context. Is it the boundary of ? So the corrected version specifies these three things?
: includes its own boundary.
: the boundary of A lies wholly on the boundary of .
: doesn't intersect the boundary of anywhere except at its own boundary.
The last one would mean, for example, that a bounded area on the surface of a ball doesn't meet the condition, but a slice through the ball does.
If I've got that right, it would be nice to spell the three points out explicitly, for the benefit of people who are interested in the ideas but don't easily see them from the notation.