Topological Degree in Finite Dimensions

Klaus Deimling
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Klaus Deimling: Gesamthochschule Paderborn

Chapter Chapter 1 in Nonlinear Functional Analysis, 1985, pp 1-34 from Springer

Abstract: Abstract In this basic chapter we shall study some basic problems concerning equations of the form f (x) = y, where f is a continuous map from a subset Ω ⊂ ℝ n into ℝ n and y is a given point in ℝ n . First of all we want to know whether such an equation has at least one solution x ∈Ω. If this is the case for some equation, we are then interested in the question of whether this solution is unique or not. We then also want to decide how the solutions are distributed in Ω. Once we have some answers for a particular equation, we need also to study whether these answers remain the same or change drastically if we change f and y in some way. It is most probable that you have already been confronted, more or less explicitly, by all these questions at this stage in your mathematical development.

Keywords: Topological Vector Space; Negative Eigenvalue; Continuous Extension; Finite Dimension; Product Formula (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-3-662-00547-7_1

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