Orientable Surface

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orientable surface

[‚ȯr·ē‚en·tə·bəl ′sər·fəs]
(mathematics)
A surface for which an object resting on one side of it cannot be moved continuously over it to get to the other side without going around an edge.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Orientable Surface

a surface that can be oriented. An orientable surface is the opposite of a nonorientable surface. On a nonorientable surface, for example, a Möbius band, there always exist closed curves such that the orientation of a small neighborhood of a point moving along the curve is reversed when the entire curve is traversed. The projective plane is an important example of a closed nonorientable surface.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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([s.sub.5]) Orientability of the focus in the right half-plane.
Here we have used the the MSp orientability of the bundle 4[eta] over [RP.sup.[infinity]] to identify [Mathematical Expression Omitted]([RP.sup.[infinity].sub.4] with [MSp.sup.*-4](RP.sup.[infinity]], and have chosen the Thom class in [Mathematical Expression Omitted] to be an extension of x; thus the second homomorphism in the exact sequence is multiplication by [chi].
Chambolle, in particular for discussions about (1.20) and orientability. He wishes to acknowledge support from the Institut Universitaire de France, and the grant ANR-12-BS01-0014-01 "GEOMETRYA".
Samelson, Orientability of hypersurfaces in [R.sup.n].
(2) It is possible that the orientability assumption can be eliminated.
Moreover, if the manifold at issue really were 'bare', there would be no more notion of betweenness than there would be of momentum; Earman and Norton assume, however, that the manifold has a differentiable structure, and the diffeomorphisms they discuss will preserve not only the relations they name, but also structures that I do not suppose anyone would call observable: do we observe the smoothness of functions, or global orientability, or compactness?
The high molecular weight "tail" also provides the possibility of higher tenacity and orientability in these applications.
It has been suggested that the orientation developed in the die is slight and reflects the poor orientability associated with shear flow (9).
An analogy can be drawn with solid-state deformation processes for the injection molded samples studied here, where the "melt orientability" acts like a melt draw ratio.

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