منابع مشابه
Computational Differential Topology
Some of the more differential aspects of the nascent field of computational topology are introduced and treated in considerable depth. Relevant categories based upon stratified geometric objects are proposed, and fundamental problems are identified and discussed in the context of both differential topology and computer science. New results on the triangulation of objects in the computational di...
متن کاملComputational Topology Surface Topology Afra
Last lecture, we spent a considerable amount of effort defining manifolds. We like manifolds because they are locally Euclidean. So, even though it is hard for us to reason about them globally, we know what to do in small neighborhoods. It turns out that this ability is all we really need. This is rather fortunate, because we suddenly have spaces with more interesting structure than the Euclide...
متن کاملComputational Topology
The authors of this article believe there is or should be a research area appropriately referred to as computa tional topology Its agenda includes the identi cation and formalization of topological questions in computer applications and the study of algorithms for topolog ical problems It is hoped this article can contribute to the creation of a computational branch of topology with a unifying ...
متن کاملComputational Topology
According to the Oxford English Dictionary, the word topology is derived of topos (tìpo ) meaning place, and -logy (logia), a variant of the verb légein, meaning to speak. As such, topology speaks about places: how local neighborhoods connect to each other to form a space. Computational topology, in turn, undertakes the challenge of studying topology using a computer. The field of geometry stud...
متن کاملDifferential Topology
This paper is to propose solutions to selected exercises in Differential Topology by Guillemin and Pollack, [1], and to comment on certain proofs in the book. Although the sections covered in this paper correspond to specific sections in the book, they have been freely renamed to suit the content. The sections of the book which will be covered here are, in order: §6: Homotopy and Stability Appe...
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ژورنال
عنوان ژورنال: Applied General Topology
سال: 2007
ISSN: 1989-4147,1576-9402
DOI: 10.4995/agt.2007.1909