منابع مشابه
Some Mappings with Topological Degree Zero
is sometimes proved by determining the topological degree of M at q. If the degree is different from zero, the equation has a solution. However if the degree is zero, then purely topological considerations give practically no information about solutions. The advantage of the topological degree approach is that comparatively little information about the mapping is needed. In this note we study l...
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1. In previous papers [2; 3], the problem of proving an existence theorem for a certain functional equation was reduced to that of computing the topological degree of a mapping in Euclidean w-space defined by homogeneous polynomials or infinite series. The complex case of the latter problem was solved in [4]. Since the problem is analogous to that of studying the roots of a polynomial equation,...
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We prove a finiteness result for the ∂-patterned guts decomposition of all 3manifolds obtained by splitting a given orientable, irreducible and ∂-irreducible 3manifold along a closed incompressible surface. Then using the Thurston norm, we deduce that the JSJ-pieces of all 3-manifolds dominated by a given compact 3-manifold belong, up to homeomorphism, to a finite collection of compact 3-manifo...
متن کاملThe Topological Degree for Noncompact Nonlinear Mappings in Banach Spaces
Let X and Y be Banach spaces, G an open subset of X. If we denote the closure of G by cl(G), let ƒ be a mapping of cl(G) into Y. For X~ Y and ƒ a compact mapping, Leray and Schauder [9] gave a definition of topological degree for mappings of the form ƒ —ƒ on the open set G over a point a of X whenever (I—f)"^) is a compact subset of G. The Leray-Schauder degree for compact displacements is the ...
متن کاملSome Elementary Applications of Topological Degree
In this paper we consider the degree theory for a mapping f from an oriented compact connected manifold X to a oriented, compact, connected manifold Y of the same dimension and some elementary problems of fixed points. 1. Topological degree on manifolds. There are many approaches to the introduction of the notion of degree and the background involved in each of them may differ considerably.We b...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1956
ISSN: 0002-9939
DOI: 10.2307/2033055