A Retraction Theorem

Robert F. Brown

Chapter Chapter 14 in A Topological Introduction to Nonlinear Analysis, 2014, pp 103-107 from Springer

Abstract: Abstract Let’s begin with an example. Inside the linear space C[0, 1] of maps u : [ 0 , 1 ] → R $$u: [0,1] \rightarrow \mathbf{R}$$ is the positive cone of C[0, 1], written C +[0, 1], which is the set of all u ∈ C[0, 1] such that u(t) ≥ 0 for all t. The positive cone is obviously convex and it is a closed subset of C[0, 1] with respect to the sup norm because if u 0 ( t 0 )

Keywords: Retraction Theorem; Positive Cone; Normed Linear Space; Epsilon Neighborhood; Open Cover (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-11794-2_14

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