The purpose of this paper is to prove Theoreme: Of two concentric circles C_1 and C_2, let C_1 be the smaller. Denote by H the point set which is the sum of C_1, C_2, and the annular domain bounded by C_1 and C_2. Let M be a continuum which contains a point A interior to C_1 and a point B exterior to C_2. If N is any connected subset of M containing A and B, N will contain at least one point of some continuum which is a subset of M and H, and which has at least one point in common with each of the circles C_1 and C_2.
@article{bwmeta1.element.bwnjournal-article-fmv7i1p27bwm,
author = {R. Wilder},
title = {A theorem on continua},
journal = {Fundamenta Mathematicae},
volume = {7},
year = {1925},
pages = {311-313},
zbl = {51.0462.05},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv7i1p27bwm}
}
Wilder, R. A theorem on continua. Fundamenta Mathematicae, Tome 7 (1925) pp. 311-313. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv7i1p27bwm/