A characterisation of a continuous curve
Tom 7 / 1925
Fundamenta Mathematicae 7 (1925), 302-307
DOI: 10.4064/fm-7-1-302-307
Streszczenie
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.
