Talk:Neat submanifold

The revision of 20:44 26 August 2018 created an error which should be reverted: The definition of neat submanifold should require $\partial A=A\cap \partial M$, not $\partial A\subset \partial M$.

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".

--Mosher (talk) 14:31, 17 June 2021 (UTC)

I'm unfamiliar with what $\partial A$ represents in this context. Is it the boundary of $A$? So the corrected version specifies these three things?

$\partial A\subset A$: $A$ includes its own boundary.

$\partial A\subset \partial M$: the boundary of A lies wholly on the boundary of $M$.

$A\cap \partial M\subset \partial A$: $A$ doesn't intersect the boundary of $M$ 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.

Musiconeologist (talk) 18:24, 25 September 2021 (UTC)