The purpose of this paper is to prove: Théorème: In order that a continuum M should be a continuous curve it is necessary and sufficient that for every two distinct points A and B of M there should exist a subset of M which consists of a finite number of continua and which separates A from B in M. Théorème: In order that a bounded continuum M should be a continuous curve which contains no domain and does not separate the plane it is necessary and sufficient that for every two distinct points A and B which belong to M there should exist a point which separates A from B in M.
@article{bwmeta1.element.bwnjournal-article-fmv7i1p25bwm,
author = {R. Moore},
title = {A characterisation of a continuous curve},
journal = {Fundamenta Mathematicae},
volume = {7},
year = {1925},
pages = {302-307},
zbl = {51.0462.04},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv7i1p25bwm}
}
Moore, R. A characterisation of a continuous curve. Fundamenta Mathematicae, Tome 7 (1925) pp. 302-307. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv7i1p25bwm/