Sard’s Theorem

Rajnikant Sinha ()
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Rajnikant Sinha: Magadh University, Department of Mathematics

Chapter Chapter 6 in Smooth Manifolds, 2014, pp 431-476 from Springer

Abstract: Abstract The root of Sard’s theorem lies in real analysis. It is one of the deep results in real analysis. How this result can be generalized into the realm of smooth manifold theory is only a later development. Its importance in manifold theory is for a definite reason. Upon applying Sard’s theorem, Whitney was able to prove a startling property about smooth manifolds: For every smooth manifold, ambient space can be constructed, etc. For pedagogical reasons, we have given its proof in step-by-step manner using Taylor’s inequality. Largely, this chapter is self-contained.

Keywords: Smooth Manifold Theory; Real Analysis; Pedagogical Reasons; Definite Reason; Ambient Space (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-81-322-2104-3_6

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