Manifolds

Serge Lang
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Serge Lang: Yale University, Department of Mathematics

Chapter Chapter II in Differential Manifolds, 1985, pp 21-40 from Springer

Abstract: Abstract Starting with open subsets of Banach spaces, one can glue them together with C p -isomorphisms. The result is called a manifold. We begin by giving the formal definition. We then make manifolds into a category, and discuss special types of morphisms. We define the tangent space at each point, and apply the criteria following the inverse function theorem to get a local splitting of a manifold when the tangent space splits at a point.

Keywords: Banach Space; Open Subset; Tangent Space; Open Neighborhood; Half Plane (search for similar items in EconPapers)
Date: 1985
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DOI: 10.1007/978-1-4684-0265-0_2

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