View source for Delta-sigma-operation

{{TEX|done}}{{MSC|03E15}}

''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|Descriptive set theory]].

====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 $\delta s$ operation"  ''Russian Math. Surveys'' , '''21''' :  4  (1966)  pp. 247–250  ''Uspekhi Mat. Nauk'' , '''21''' :  4  (1966)  pp. 275–278</TD></TR></table>