The main purpose of the present paper is to show that if a bounded continuum has more then one prime part and no one of its prime parts separates the plane then in order that it should have just two complementary domains and be the complete boundary of each of them it is necessary and sufficient that it should remain connected in the weak sense on the removal of any one of its connected proper subsets which is closed.
@article{bwmeta1.element.bwnjournal-article-fmv6i1p22bwm,
author = {R. Moore},
title = {Concerning the common boundary of two domains},
journal = {Fundamenta Mathematicae},
volume = {6},
year = {1924},
pages = {203-213},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv6i1p22bwm}
}
Moore, R. Concerning the common boundary of two domains. Fundamenta Mathematicae, Tome 6 (1924) pp. 203-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv6i1p22bwm/