Abstract
Associated with each real valued function of several real variables is a collection of sets, callcd level sets, which are useful in studying qualitative properties of the function. Given a function f: U → ℝ. where U ⊂ ℝn +1,its level sets are the sets f-1 (c) defined, for each real number c, by
. The number c is called the height of the level set, and f-1(c) is called the level set at height c. Since f-l(c) is the solution set of the equation f(x1…, x n +1) = c, the level set f-1(c) is often described as “the set f(x1,…, x n +1) = c.”
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1979 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Thorpe, J.A. (1979). Graphs and Level Sets. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_1
Download citation
DOI: https://doi.org/10.1007/978-1-4612-6153-7_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
Online ISBN: 978-1-4612-6153-7
eBook Packages: Springer Book Archive