Delta-sigma-operation

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