Manifolds with Boundary

Antonio Villanacci, Laura Carosi, Pierluigi Benevieri and Andrea Battinelli
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Antonio Villanacci: Università degli Studi di Firenze
Laura Carosi: Università degli Studi di Pisa
Pierluigi Benevieri: Università degli Studi di Firenze
Andrea Battinelli: Università degli Studi di Siena

Chapter Chapter 5 in Differential Topology and General Equilibrium with Complete and Incomplete Markets, 2002, pp 107-132 from Springer

Abstract: Abstract According to our definition of C r manifold, given in Chapter 2, we cannot use our “differential topology tool kit” for many interesting sets such as a closed unit ball, a solid torus, a compact cylindrical surface. Those sets fail to be C r manifolds because of points they have on their “boundaries”. In fact, around those points they look like closed euclidean halfspaces or even convex cones. The definition of manifold with boundary deals with this issue, encompassing a wider class of objects which includes some of the examples we have just referred to.

Keywords: Open Subset; Tangent Space; General Equilibrium; Local Parametrization; Inverse Image (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-1-4757-3619-9_5

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