Difference between revisions of "Delta-sigma-operation"
From Encyclopedia of Mathematics
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| − | + | ''Hausdorff operation'' | |
| − | where | + | 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|Descriptive set theory]]. | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.N. Kolmogorov, "On operations over sets" ''Mat. Sb.'' , '''35''' : 3–4 (1928) pp. 415–422 (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> W. Hayes, R. Probstein, "Hypersonic flow theory" , New York-London (1959)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> P.S. Aleksandrov, "Theory of functions of a real variable and the theory of topological spaces" , Moscow (1978) (In Russian)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> Yu.S. Ochan, "The theory of operations over sets" ''Uspekhi Mat. Nauk'' , '''10''' : 3 (1955) pp. 71–128 (In Russian)</TD></TR><TR><TD valign="top">[5]</TD> <TD valign="top"> A.N. Kolmogorov, "P.S. Alexandroff and the theory of the | + | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.N. Kolmogorov, "On operations over sets" ''Mat. Sb.'' , '''35''' : 3–4 (1928) pp. 415–422 (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> W. Hayes, R. Probstein, "Hypersonic flow theory" , New York-London (1959)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> P.S. Aleksandrov, "Theory of functions of a real variable and the theory of topological spaces" , Moscow (1978) (In Russian)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> Yu.S. Ochan, "The theory of operations over sets" ''Uspekhi Mat. Nauk'' , '''10''' : 3 (1955) pp. 71–128 (In Russian)</TD></TR><TR><TD valign="top">[5]</TD> <TD valign="top"> 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</TD></TR></table> |
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=14155
Delta-sigma-operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Delta-sigma-operation&oldid=14155
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