Interpolation and approximation from sublattices of C₀(X; R)
DOI:
https://doi.org/10.22199/issn.0717-6279-2019-03-0025Keywords:
Bonsall, Lattices, Interpolation, ApproximationAbstract
In this paper, we give a proof of a result concerning simultaneous interpolation and approximation from sublattices of the space of real continuous functions vanishing at infinity.
References
S. Boel, T. Carlsen and N. Hansen, "A Useful Strengthening of the Stone-Weierstrass Theorem", The American Mathematical Monthly, vol. 108, no. 7, p. 642, 2001, doi: 10.2307/2695271.
F. Bonsall, "Semi-Algebras of Continuous Functions", Proceedings of the London Mathematical Society, vol. s3-10, no.1, pp. 122-140, 1960, doi: 10.1112/plms/s3-10.1.122.
F. Deutsch, "Simultaneous Interpolation and Approximation in Topological Linear Spaces", SIAM Journal on Applied Mathematics, vol. 14, no. 5, pp. 1180-1190, 1966, doi: 10.1137/0114095.
W. Rudin, Real and complex analysis, 3rd ed. Singapore: McGraw-Hill, 1987.
G. Simmons, Introduction to topology and modern analysis. New York: McGraw-Hill, 1963.
H. Wu, "New Stone-Weierstrass Theorem", Advances in Pure Mathematics, vol. 06, no. 13, pp. 943-947, 2016, doi: 10.4236/apm.2016.613071.
Published
How to Cite
Issue
Section
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.