A characterisation of a continuous curve

Moore, R.. "A characterisation of a continuous curve." Fundamenta Mathematicae 7.1 (1925): 302-307. <http://eudml.org/doc/214581>.

@article{Moore1925,
abstract = {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.},
author = {Moore, R.},
journal = {Fundamenta Mathematicae},
keywords = {zbiór spójny; krzywa ciągła; zbiór rozdzielający; topologia; continuum},
language = {eng},
number = {1},
pages = {302-307},
title = {A characterisation of a continuous curve},
url = {http://eudml.org/doc/214581},
volume = {7},
year = {1925},
}

TY - JOUR
AU - Moore, R.
TI - A characterisation of a continuous curve
JO - Fundamenta Mathematicae
PY - 1925
VL - 7
IS - 1
SP - 302
EP - 307
AB - 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.
LA - eng
KW - zbiór spójny; krzywa ciągła; zbiór rozdzielający; topologia; continuum
UR - http://eudml.org/doc/214581
ER -