Geodesic
Metrization of the space of all simple rings in the region of family $\mathfrak B$
Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 607-618.

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The problem involved with metrizing space $\Sigma$ is solved. In particular, it is shown that simple rings in the sequence of plane regions $(B_n)$ converging to kernel $B_0$ can be introduced by properly metrizing the set $\bigcup\limits_{n=0}^\infty{B_n}$. 
@article{MZM_1969_6_5_a11,
     author = {B. P. Kufarev},
     title = {Metrization of the space of all simple rings in the region of family $\mathfrak B$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {607--618},
     publisher = {mathdoc},
     volume = {6},
     number = {5},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a11/}
}
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B. P. Kufarev. Metrization of the space of all simple rings in the region of family $\mathfrak B$. Matematičeskie zametki, Tome 6 (1969) no. 5, pp. 607-618. http://geodesic.mathdoc.fr/item/MZM_1969_6_5_a11/