AHLFORS SARIO RIEMANN SURFACES DOWNLOAD!
PDF | On Jan 1, , George Springer and others published Review: Lars V. Ahlfors and Leo Sario, Riemann surfaces. Riemann surfaces. By Lars V. Ahlfors and Leo Sario. The fundamental group, the index of a curve, the degree of a mapping, and orientability of a surface are introduced and a rather extensive treatment of cover- ing surfaces follows. Review: Lars V. Ahlfors and Leo Sario, Riemann surfaces. Bull. Amer. Math. Soc. 67 , no. 2,
|Published:||16 August 2016|
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Lars V. Ahlfors, L. Sario - Riemann Surfaces
For this reason the topological theory of surfaces belongs in this book. There is a great temptation to bypass the finer deta. The ahlfors sario riemann surfaces demerit of this approach is that it does not yield complete results.
For instance, it cannot be proved by analytical means that every surface which satisfies the axiom of countability can be made into a Riemann surface. In other instances the analytical method becomes so involved that it no longer possesses ahlfors sario riemann surfaces merit of elegance.
For complete results this derivation must be based on the method of triangulation. On the other hand, it is much easier to obtain superficial knowledge without use of triangulations, for instance, by the method of singular homology.
It so happens that this superficial knowledge is adequate for most applications to the theory of Riemann surfaces, and our presentation is influenced by this fact. Since we ahlfors sario riemann surfaces for completeness, a considerable part of the first chapter has been allotted to the oombinatorial approach.
Riemann Surfaces - Lars V. Ahlfors, Leo Sario - Google книги
We have tried, however, to isolate this pq. This is done by formulating the combinatorial theory as a theory of triangulated surfaces, or polyhedrons.
This elementary section has been included for the sakP of l"ompleteness and because beginning analysts are not always well prepared on this point. The section can of course be o.
The fundamental group is introduced, and the notion of bordE. The chapter closes with the construction of a triangulation.
If there arc no relations between the points, pure set theory exhausts all poRsibilities.
Lars V. Ahlfors, L. Sario - Riemann Surfaces - livro em pdf
As soon as one wants to go beyond set theory to limits and continuity it becomes necessary to introduce a topology, and the space becomes a topological ahlfors sario riemann surfaces. The following conditions shall be fulfilled: AI The union of any collldion of open sets is open. A2 The intersection of any finite coUection of open sets is open.
The ahlfors sario riemann surfaces are interpreted to hold also for the empty collection. According ahlfors sario riemann surfaces usual conventions the union of an empty collection of sets is the empty set 0, and the intersection of an empty collection is the whole space 8.
Hence AI and A2 imply that 0 and 8 are open. In most a third requirement is added: It is therefore convenient to introduce the notion of a basis for the open sets briefly: Such a basis is a system fJI of subsets of 8 which satisfies condition B The intersection of any finite collldion of sets in fJI is a union of sets in