Difference between revisions of "Delta-sigma-operation"
From Encyclopedia of Mathematics
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A set-theoretic operation, the result of its application to a sequence $(E_n)$ of sets can be noted thus: | A set-theoretic operation, the result of its application to a sequence $(E_n)$ of sets can be noted thus: | ||
Latest revision as of 17:25, 1 January 2021
2020 Mathematics Subject Classification: Primary: 03E15 [MSN][ZBL]
Hausdorff operation
A set-theoretic operation, the result of its application to a sequence $(E_n)$ of sets can be noted thus:
$$\Phi(E_n)=\bigcup_{z\in N}\bigcap_{n\in z}E_n,$$
where $N$ is a system of sets of positive integers, called the base of the $\delta$-$\sigma$-operation. See Descriptive set theory.
References
| [1] | A.N. Kolmogorov, "On operations over sets" Mat. Sb. , 35 : 3–4 (1928) pp. 415–422 (In Russian) |
| [2] | W. Hayes, R. Probstein, "Hypersonic flow theory" , New York-London (1959) |
| [3] | P.S. Aleksandrov, "Theory of functions of a real variable and the theory of topological spaces" , Moscow (1978) (In Russian) |
| [4] | Yu.S. Ochan, "The theory of operations over sets" Uspekhi Mat. Nauk , 10 : 3 (1955) pp. 71–128 (In Russian) |
| [5] | A.N. Kolmogorov, "P.S. Alexandroff and the theory of the $\delta s$ operation" Russian Math. Surveys , 21 : 4 (1966) pp. 247–250 Uspekhi Mat. Nauk , 21 : 4 (1966) pp. 275–278 |
How to Cite This Entry:
Delta-sigma-operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delta-sigma-operation&oldid=32854
Delta-sigma-operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delta-sigma-operation&oldid=32854
This article was adapted from an original article by A.G. El'kin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article