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results of u,s government may have serious negative effects on the global economy. Also featured in the programme are Dr. Piyush Gupta, Professor. Please note that the information provided by the author(s) is .Q:

“Rewriting” an (oriented) surface

Let us first state a classical theorem. It can be found in Topology from an Advanced
Geometric Viewpoint by R.M.Smale
Lemma
Let $S$ be an oriented surface. Then we can find an oriented surface $N$, such that:

There is an orientation preserving homeomorphism between $S$ and $N$,
There is an orientation preserving diffeomorphism between $S$ and $N$.

In fact, we can assume that $N$ is a cube and it suffices to find, for each face, an orientation preserving homeomorphism to cover the corresponding face of $S$.
Problem
Let us continue. Let $S$ be a closed connected oriented surface. Fix an orientation on $S$.
Question
Is it possible to “rewrite” $S$ (without changing its orientation) so that it becomes equal to a plane in its re-written version?
Basically, I want to find a sequence of homeomorphisms that shrink the surface $S$ while preserving the orientation. I also want the homeomorphisms to “really” shrink the surface, so I need continuity.
P.S. I apologize for this “general” question. If it seems it is too general, then I will add more details in my comment at your answer.

A:

Another possible answer is through the use of self-indexing triangulations. A self-indexing triangulation of a closed 2-manifold is basically just a collection of smaller versions of the surface. As such, you can’swap out’ a triangle for a square to basically get a rectangle that’s already a plane. However, a self-indexing triangulation of an open surface must be a regular one, which is also a plane. A regular self-indexing triangulation of a surface is a subdivision of the surface into triangles, and is called a mesh.

and even a barbed wire fence. The place is shown on the internet, but the exact locations are not indicated. The Catholic monks won’t give up the records, because they say they
d0c515b9f4

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