manifolds

You probably mean bounded manifolds—the plane is closed (it contains all its limit points).

If you have d-dimensional manifolds A and B, a cobordism between them is a (d+1)-dimensional manifold-with-boundary (what does that mean?

Furthermore, the cost of producing the gas is not just the cost of the vessel - you need to drill wells and connect them to the vessel via pipelines/manifolds/risers.

You can extend this to k-D manifolds on n-D spaces by normalizing this volume with a n-k dimensional ball.

Also hoods are often replaced for carbon in racing and a lot of people have exhaust manifolds directly below them.

You want definitions of continuity and differentiability that generalize nicely to arbitrary dimension, to manifolds, to Lie groups, to whatever.

But that's not as important as the idea that the points composing the manifolds in question represent distinct probability distributions.

One usually wants to do differential geometry on manifolds, that is have some notion of first/second/higher order geometry, in other words do all the things one knows and loves from calculus/analysis on manifolds.

In 1987, BMW introduced the 1988 model year 750i, with a V12 engine that has two intake manifolds and two throttle valves.

Are you excluding things like 'continuity' from calculus because sure, you get topologies on discrete spaces and such, but on the other hand: manifolds.

So the double edge detection will give you manifolds, which is good.

But then I go to wikipedia get hit with differential geometry, manifolds, multi-linear algebra, etc...

"Click on all of the icons below that represent animals." Anyone else notice that only the animals are simply-connected 2-manifolds?

Is it not enough to say "Ok, continuous functions over complex manifolds are interesting compared to the functions you learned in high school (like y=x^2+x+1) because they are restricted to certain behaviors, which makes them easy to predict"?

A cobordism between them is given by a hollow ball; one sphere is its outer surface, one its inner surface.) I have no knowledge of the details, but it turns out (and was proved in the 1970s) that "all manifolds in dimension 5 and up are triangulable" is equivalent to a rather technical statement about homology and cobordisms (in, curiously, only 3 dimensions).

Then for more, popular is Spivak, 'Calculus on Manifolds', mostly because it is short.

Manifolds have no thickness, but they do have area.